How to find the perimeter of an equilateral triangle - Math

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Question

A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?

The inner angles of the corner triangles is 30°.

Answer

There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

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Question

The height of an equilateral triangle is $\dpi{100} \small 2\sqrt{3}$

What is the triangle's perimeter?

Answer

An altitude drawn in an equilateral triangle will form two 30-60-90 triangles. The height of equilateral triangle is the length of the longer leg of the 30-60-90 triangle. The length of the equilateral triangle's side is the length of the hypotenuse of the 30-60-90.

The ratio of the length of the hypotenuse to the length of the longer leg of a 30-60-90 triangle is $\dpi{100} \small 2:\sqrt{3}$

The length of the longer leg of the 30-60-90 triangle in this problem is $\dpi{100} \small 2\sqrt{3}$

Using this ratio, we find that the length of this triangle's hypotenuse is 4. Thus the perimeter of the equilateral triangle will be 4 multiplied by 3, which is 12.

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Question

An equilateral triangle has a side length of $s=\sqrt{3}$ . What is its perimeter?

Answer

An equilateral triangle possesses three sides of equal lengths. Therefore, we can easily calculate its perimeter by tripling the given side length.

$P=3*\sqrt{3}$

$\rightarrow 5.20$

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Question

An equilateral triangle has an altitude length of $h=2\sqrt{3}$ . What is its perimeter?

Answer

An altitude slices an equilateral triangle into two $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. These triangles follow a side length pattern. The smallest of the two legs equals and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or $h=x\sqrt{3}$ .

We have the length of the altitude of the triangle $h=\sqrt{3}$ . We can solve for the smallest side via substitution and simple algebra.

$h=x\sqrt{3}$

$2\sqrt{3}=x\sqrt{3}$

$x=\frac{2\sqrt{3}}{\sqrt{3}}$

Note, this is only the smallest side of one of the $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. It needs to be doubled to equal a complete side of the equilateral triangle.

Now, the side length can be tripled to calculate the perimeter.

$\rightarrow12$

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Question

Find the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

Where is the length of the side

Plugging in our values, we get:

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Question

Determine the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

,

where is the length of the side.

Plugging in our value, we get:

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Question

An equilateral triangle has a side of length feet. What is the perimeter of the triangle?

Answer

An equilateral triangle by definition. has three congruent sides. Thus, if one side is feet long, then all three sides are each feet long. We also know that the perimeter is the sum of all sides. Therefore, our perimeter is

Since we were given units of feet, our final answer is feet.

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Question

A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?

The inner angles of the corner triangles is 30°.

Answer

There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

Compare your answer with the correct one above

Question

The height of an equilateral triangle is $\dpi{100} \small 2\sqrt{3}$

What is the triangle's perimeter?

Answer

An altitude drawn in an equilateral triangle will form two 30-60-90 triangles. The height of equilateral triangle is the length of the longer leg of the 30-60-90 triangle. The length of the equilateral triangle's side is the length of the hypotenuse of the 30-60-90.

The ratio of the length of the hypotenuse to the length of the longer leg of a 30-60-90 triangle is $\dpi{100} \small 2:\sqrt{3}$

The length of the longer leg of the 30-60-90 triangle in this problem is $\dpi{100} \small 2\sqrt{3}$

Using this ratio, we find that the length of this triangle's hypotenuse is 4. Thus the perimeter of the equilateral triangle will be 4 multiplied by 3, which is 12.

Compare your answer with the correct one above

Question

An equilateral triangle has a side length of $s=\sqrt{3}$ . What is its perimeter?

Answer

An equilateral triangle possesses three sides of equal lengths. Therefore, we can easily calculate its perimeter by tripling the given side length.

$P=3*\sqrt{3}$

$\rightarrow 5.20$

Compare your answer with the correct one above

Question

An equilateral triangle has an altitude length of $h=2\sqrt{3}$ . What is its perimeter?

Answer

An altitude slices an equilateral triangle into two $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. These triangles follow a side length pattern. The smallest of the two legs equals and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or $h=x\sqrt{3}$ .

We have the length of the altitude of the triangle $h=\sqrt{3}$ . We can solve for the smallest side via substitution and simple algebra.

$h=x\sqrt{3}$

$2\sqrt{3}=x\sqrt{3}$

$x=\frac{2\sqrt{3}}{\sqrt{3}}$

Note, this is only the smallest side of one of the $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. It needs to be doubled to equal a complete side of the equilateral triangle.

Now, the side length can be tripled to calculate the perimeter.

$\rightarrow12$

Compare your answer with the correct one above

Question

Find the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

Where is the length of the side

Plugging in our values, we get:

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Question

Determine the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

,

where is the length of the side.

Plugging in our value, we get:

Compare your answer with the correct one above

Question

An equilateral triangle has a side of length feet. What is the perimeter of the triangle?

Answer

An equilateral triangle by definition. has three congruent sides. Thus, if one side is feet long, then all three sides are each feet long. We also know that the perimeter is the sum of all sides. Therefore, our perimeter is

Since we were given units of feet, our final answer is feet.

Compare your answer with the correct one above

Question

A square rug border consists of a continuous pattern of equilateral triangles, with isosceles triangles as corners, one of which is shown above. If the length of each equilateral triangle side is 5 inches, and there are 40 triangles in total, what is the total perimeter of the rug?

The inner angles of the corner triangles is 30°.

Answer

There are 2 components to this problem. The first, and easier one, is recognizing how much of the perimeter the equilateral triangles take up—since there are 40 triangles in total, there must be 40 – 4 = 36 of these triangles. By observation, each contributes only 1 side to the overall perimeter, thus we can simply multiply 36(5) = 180" contribution.

The second component is the corner triangles—recognizing that the congruent sides are adjacent to the 5-inch equilateral triangles, and the congruent angles can be found by

180 = 30+2x → x = 75°

We can use ratios to find the unknown side:

75/5 = 30/y → 75y = 150 → y = 2''.

Since there are 4 corners to the square rug, 2(4) = 8'' contribution to the total perimeter. Adding the 2 components, we get 180+8 = 188 inch perimeter.

Compare your answer with the correct one above

Question

The height of an equilateral triangle is $\dpi{100} \small 2\sqrt{3}$

What is the triangle's perimeter?

Answer

An altitude drawn in an equilateral triangle will form two 30-60-90 triangles. The height of equilateral triangle is the length of the longer leg of the 30-60-90 triangle. The length of the equilateral triangle's side is the length of the hypotenuse of the 30-60-90.

The ratio of the length of the hypotenuse to the length of the longer leg of a 30-60-90 triangle is $\dpi{100} \small 2:\sqrt{3}$

The length of the longer leg of the 30-60-90 triangle in this problem is $\dpi{100} \small 2\sqrt{3}$

Using this ratio, we find that the length of this triangle's hypotenuse is 4. Thus the perimeter of the equilateral triangle will be 4 multiplied by 3, which is 12.

Compare your answer with the correct one above

Question

An equilateral triangle has a side length of $s=\sqrt{3}$ . What is its perimeter?

Answer

An equilateral triangle possesses three sides of equal lengths. Therefore, we can easily calculate its perimeter by tripling the given side length.

$P=3*\sqrt{3}$

$\rightarrow 5.20$

Compare your answer with the correct one above

Question

An equilateral triangle has an altitude length of $h=2\sqrt{3}$ . What is its perimeter?

Answer

An altitude slices an equilateral triangle into two $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. These triangles follow a side length pattern. The smallest of the two legs equals and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or $h=x\sqrt{3}$ .

We have the length of the altitude of the triangle $h=\sqrt{3}$ . We can solve for the smallest side via substitution and simple algebra.

$h=x\sqrt{3}$

$2\sqrt{3}=x\sqrt{3}$

$x=\frac{2\sqrt{3}}{\sqrt{3}}$

Note, this is only the smallest side of one of the $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. It needs to be doubled to equal a complete side of the equilateral triangle.

Now, the side length can be tripled to calculate the perimeter.

$\rightarrow12$

Compare your answer with the correct one above

Question

Find the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

Where is the length of the side

Plugging in our values, we get:

Compare your answer with the correct one above

Question

Determine the perimeter of the following equilateral triangle:

Answer

The formula for the perimeter of an equilateral triangle is:

,

where is the length of the side.

Plugging in our value, we get:

Compare your answer with the correct one above

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