Equilateral Triangles

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SSAT Upper Level Quantitative › Equilateral Triangles

Questions 1 - 10

The perimeter of an equilateral triangle is 39 meters. In meters, how long is one side of the triangle?

Explanation

An equilateral triangle has sides that are the same length. Then, to find the length of one side, you only need to divide the perimeter by 3.

$39\div3=13$

The perimeter of an equilateral triangle is 39 meters. In meters, how long is one side of the triangle?

Explanation

An equilateral triangle has sides that are the same length. Then, to find the length of one side, you only need to divide the perimeter by 3.

$39\div3=13$

The length of one side of an equilateral triangle is . In meters, what is the perimeter of this triangle?

Explanation

Since an equilateral triangle has equal side lengths, multiply the length of one side by to find the perimeter.

$15\times3=45$

The length of one side of an equilateral triangle is . In meters, what is the perimeter of this triangle?

Explanation

Since an equilateral triangle has equal side lengths, multiply the length of one side by to find the perimeter.

$15\times3=45$

An equilateral triangle has sides of length . Find the measure of the height for this triangle.

$3\sqrt3$

$3\sqrt2$

$\sqrt3$

Explanation

Triangle

The height of an equilateral triangle will always cut the side it intersects in half. Now, this is just a matter of applying the Pythagorean Theorem.

$6^2=3^2+\text{height}^2$

$\text{height}^2=27$

$\text{height}=3\sqrt3$

An equilateral triangle has sides of length . Find the measure of the height for this triangle.

$3\sqrt3$

$3\sqrt2$

$\sqrt3$

Explanation

Triangle

The height of an equilateral triangle will always cut the side it intersects in half. Now, this is just a matter of applying the Pythagorean Theorem.

$6^2=3^2+\text{height}^2$

$\text{height}^2=27$

$\text{height}=3\sqrt3$

A side of an equilateral triangle has a length of . What is the perimeter of the triangle?

Explanation

Since an equilateral triangle has equal side lengths, multiply one side length by to find the perimeter.

$12r\times3=36r$

A side of an equilateral triangle has a length of . What is the perimeter of the triangle?

Explanation

Since an equilateral triangle has equal side lengths, multiply one side length by to find the perimeter.

$12r\times3=36r$

The length of one side of an equilateral triangle is . What is the perimeter of the triangle?

Explanation

Since the side lengths of a triangle are equal, multiply the length of one side by to find the perimeter.

The perimeter of an equilateral triangle is . What is the length of one side of the triangle?

Explanation

Since an equilateral triangle has sides that are all the same, divide the perimeter by to get the length of each side.

$120t\div3=40t$

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