Calculating the length of the side of an equilateral triangle - GMAT Quantitative Reasoning

Card 0 of 4

Question

If an equilateral triangle has a perimeter of , what is the length of each side?

Answer

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :

$\frac{18}{3}= 6$

Compare your answer with the correct one above

Question

If the area of an equilateral is , given a height of , what is the base of the triangle?

Answer

We derive the equation of base of a triangle from the area of a triangle formula:

$A=\frac{bh}{2}$

$b=\frac{2A}{h}$

$b=\frac{2*12}{5}$

Compare your answer with the correct one above

Question

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

Answer

Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by

$s=\frac{2h}{\sqrt{3}}$ , where is the length of the height.

Therefore, the final answer is

$\frac{2\cdot 5}{\sqrt3}=\frac{10}{\sqrt{3}}$ .

Compare your answer with the correct one above

Question

Equilateral triangle is inscribed in a circle with radius , what is the length of a side of the triangle?

Answer

Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located $\frac{2}{3}$ away from the edge of a given height.

Therefore 5, the radius of the circle is $\frac{2}{3}$ of the height.

Therefore, the height must be $\frac{15}{2}$ .

From here, we can use the formula for the height of the equilateral triangle $h=s\frac{\sqrt{3}}{2}$ , where is the length of the height and is the length of a side of the equilateral triangle.

Therefore, $s=2\frac{h}{\sqrt{3}}$ , then $\frac{15}{\sqrt{3}}$ is the final answer.

Compare your answer with the correct one above

Tap the card to reveal the answer