Question

What is the area of an equilateral triangle whose perimeter is 48 inches?

Answer 1

Answer: `64sqrt(3)` `"in"^2`

Explanation:

Consider the formula for the area of an equilateral triangle:
`(s^2sqrt(3))/4`, where `s` is the side length (this can be easily proved by considering the 30-60-90 triangles within an equilateral triangle; this proof will be left as an exercise for the reader)

Since we are given that the perimeter of the equilateral trangle is `48` inches, we know that the side length is `48/3=16` inches.

Now, we can simply plug this value into the formula:
`(s^2sqrt(3))/4=((16)^2sqrt(3))/4`

Canceling, a `4` from the numerator and the denominator, we have:
`=(16*4)sqrt(3)`
`=64sqrt(3)` `"in"^(2)`, which is our final answer.