Question

The area of an equilateral triangle is given by A =3^1/2/4s^2. Find the length of the side s of an equilateral triangle with an area of 12^1/2 square inches.

Answer 1

Answer:

The length of the side of an equilateral traingle $s=2\sqrt{2}$ inches

Step-by-step explanation:

Given that the area of an equilateral triangle is given by

$A=3^\frac{1}{2}s^2$

It can be written as

$a=\frac{\sqrt{3}}{4} s^2$ Square inches        (1)

To find the length of the side s os an equilateral triangle

Given that area of an equilateral triangle is $12^\frac{1}{2}$ square inches

It can be written as

$A=12^\frac{1}{2}$

$A=\sqrt{12}$ square inches

It can be written as

$A=12^\frac{1}{2}$

$A=\sqrt{12}$ square inches           (2)

Now comparing equations (1) and (2) we get

$\frac{\sqrt{3}}{4}s^2=\sqrt{12}$

$\frac{\sqrt{3}}{4}s^2=\sqrt{4\times 3}$

Dividing by $\frac{\sqrt{3}}{4}$ on both sides we get

$\frac{\frac{\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}}=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{4}}$

$\frac{\sqrt{3}}{4}s^2\times\frac{4}{\sqrt{3}}=2\sqrt{3}\times\frac{4}{\sqrt{3}}$

$s^2=8$

$s=\sqrt{8}$

Therefore $s=2\sqrt{2}$ inches

Therefore the length of the side of an equilateral traingle $s=2\sqrt{2}$ inches