Calculating the perimeter of an equilateral triangle

Help Questions

GMAT Quantitative › Calculating the perimeter of an equilateral triangle

Questions 1 - 8

1

Find the perimeter of an equilateral triangle whose side length is .

Explanation

To find the perimeter, you must multiply the side length by . Thus,

2

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

Not enough information provided.

Explanation

An equilateral triangle with a side length has a perimeter .

Given:

,

.

3

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

Explanation

An equilateral triangle with a side length has a perimeter .

Given:

,

.

4

Export-png__3_

The area of an equilateral triangle is . What is the perimeter of ?

$3\sqrt{\frac{28}{\sqrt{3}}}$

$3\sqrt{\frac{16}{\sqrt{3}}}$

$\frac{28}{\sqrt{3}}$

$3\sqrt{3}$

Explanation

The area is given, which will allow us to calculate the side of the triangle and hence we can also find the perimeter.

The area for an equilateral triangle is given by the formula

$\frac{s^{2}\sqrt{3}}{4}$ , where is the length of the side of the triangle.

Therefore, $s=\sqrt{\frac{4a}{\sqrt{3}}}$ , where is the area.

Thus $s=\sqrt{\frac{28}{\sqrt{3}}}$ , and the perimeter of an equilateral triangle is three times the side, hence, the final answer is $3\sqrt{\frac{28}{\sqrt{3}}}$ .

5

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

Not enough information provided.

Explanation

An equilateral triangle with a side length has a perimeter .

Given:

,

.

6

Calculate the perimeter of an equilateral triangle whose side length is .

Explanation

To solve, simply multiply the side length by . Thus,

$P=3\cdot 3=9$

7

Given the following regarding Triangle .

I) $\small \angle H=\angle F=60^{\circ}$

II) Side is equal to light-years

What is the length of side ?

light years

light years

$\sqrt{7}$ light years

light years

light years

Explanation

The trick to this one is to carefully put together what you are given.

We know that two of our angles are equal to 60 degrees. This means that the last angle is also 60 degrees. This make HFT an equilateral triangle.

Equilateral triangles always have equal sides and equal angles, so our last side has to be 7 light years as well.

8

Calculate the perimeter of an equilateral triangle whose side length is .

Explanation

The perimeter of an equilateral triangle is:

Thus.

Return to subject