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

The length of the side of an equilateral traingle
`s=2√(2)` inches

Explanation:

Given that the area of an equilateral triangle is given by

`A=3^(1)/(2)s^2`

It can be written as

`a=(√(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^(1)/(2)` square inches

It can be written as

`A=12^(1)/(2)`

`A=√(12)` square inches

It can be written as

`A=12^(1)/(2)`

`A=√(12)` square inches (2)

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

`(√(3))/(4)s^2=√(12)`

`(√(3))/(4)s^2=√(4* 3)`

Dividing by
`(√(3))/(4)` on both sides we get

`((√(3))/(4)s^2)/((√(3))/(4))=(2√(3))/((√(3))/(4))`

`(√(3))/(4)s^2*(4)/(√(3))=2√(3)*(4)/(√(3))`

`s^2=8`

`s=√(8)`

Therefore
`s=2√(2)` inches

Therefore the length of the side of an equilateral traingle
`s=2√(2)` inches