# 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?

Jan 27, 2016

${\text{Side}}_{\square} = 8 \sqrt[4]{3}$

#### Explanation:

The semi-perimeter of the equilateral triangle is
$\textcolor{w h i t e}{\text{XXX}} s = \frac{16 + 16 + 16}{2} = 24$

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

We are told ${\text{Area"_square = "Area}}_{\triangle}$

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

and each side of the square has a length of
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{8}^{2} \sqrt{3}} = 8 \sqrt[4]{3}$