Question

Find the length of the diagonal of a square with perimeter 32.A.$4 \sqrt{2}$B. 8C.$2 \sqrt{2}$D. 45E.$8 \sqrt{2}$

Answer 1

ANSWER

$E.8\sqrt[]{2}$

EXPLANATION

The square has a perimeter of 32.

The perimeter of a square is given as:

$P=4\cdot L$

where L = length of the side of the square

Therefore, we have that for the given square:

$\begin{gathered} 32=4\cdot L \\ \Rightarrow L=\frac{32}{4} \\ L=8 \end{gathered}$

The square has sides 8 units long.

To find the length of the diagonal, apply Pythagoras theorem, since the diagonal forms a right triangle with the sides of the square:

$\text{hyp}^2=a^2+b^2$

where hyp = hypotenuse of the triangle (diagonal)

a, b = legs of the triangle (side lengths of the square)

Therefore, we have that:

$\begin{gathered} D^2=8^2+8^2 \\ D^2=64+64=128 \\ D=\sqrt[]{128} \\ D=8\sqrt[]{2} \end{gathered}$

That is the length of the diagonal.