What is the ratio of the length of a side of an equilateral triangle to its perimeter?

The area of an equilateral triangle is

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Correct answer:

Explanation:

An equilateral triangle can be broken down into 2 30-60-90 right triangles (see image). The length of a side (the base) is 2x while the length of the height is

Therefore, if 

A length of the side equals 2x:

What is the area of this triangle if 

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Correct answer:

Explanation:

We know the formula for the area of an equilateral triangle is:

if 

So, since we are told that 

Find 

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Correct answer:

Explanation:

This triangle is equilateral; we can tell because each of its sides are the same length, 

What is side 

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Correct answer:

Explanation:

Since each of this triangle's sides is equal in length, it is equilateral. To find the length of one side of an equilateral triangle, we need to divide the perimeter by 

The height of the triangle is

What is the length of the base of the triangle to the nearest tenth?

Possible Answers:

Correct answer:

Explanation:

Since it is an equilateral triangle, the line that represents the height bisects it into a 30-60-90 triangle.

Here you may use

Use the definition of an equilateral triangle to know that the answer of the hypotenuse also applies to the base of the triangle.

Therefore,

The height of an equilateral triangle is 5. How long are its sides?

Possible Answers:

Correct answer:

Explanation:

The height of an equilateral triangle, shown by the dotted line, is also one of the legs of a right triangle:

The hypotenuse is x, the length of each side in this equilateral triangle, and then the other leg is half of that, 0.5x. 

To solve for x, use Pythagorean Theorem:

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square, as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

An equilateral triangle is placed on top of a square as shown by the figure below.

Find the perimeter of the shape.

Possible Answers:

Correct answer:

Explanation:

Recall that the perimeter is the sum of all the exterior sides of a shape. The sides that add up to the perimeter are highlighted in red.

Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length.

Recall that the height of an equilateral triangle splits the triangle into 

We can then use the height to find the length of the side of the triangle.

Recall that a 

Thus, we can use the ratio and the length of the height to set up the following equation:

Plug in the given height to find the length of the side.

Now, since the perimeter of the shape consists of 

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