Question

A square and an equilateral triangle have the same perimeter. Each side of the triangle is 16 m. How do you find the length of each side of the square?

Answer 1

`"Side"_square = 8root(4)(3)`

Explanation:

The semi-perimeter of the equilateral triangle is
`color(white)("XXX")s=(16+16+16)/2 = 24`

So, by Heron's formula
`color(white)("XXX")"Area"_triangle = sqrt(24xx8xx8xx8) =8^2sqrt(3)`

We are told `"Area"_square = "Area"_triangle`

So `Area"_square = 8^2sqrt(3)`

and each side of the square has a length of
`color(white)("XXX")sqrt(8^2sqrt(3)) = 8root(4)(3)`