Question

If the perimeter of a square is 80 feet, then find the length of the diagonal.

Answer 1

20√2 ft

Explanation:

Given the perimeter of a square = 80 ft.

We want to find the length of the square's diagonal.

For a square of side length, s, the perimeter is calculated using the formula:

`\begin{gathered} P=4s \\ \implies4s=80 \\ s=(80)/(4) \\ s=20ft \end{gathered}`

The square has a side length of 20 ft.

Next, we find the length of the diagonal.

The diagonal of a square divides it into two equal right triangles as seen in the diagram above.

Using the Pythagorean theorem, we find the value of x.

`\begin{gathered} \text{Hypotenuse}^2=\text{Altitude}^2+\text{Base}^2 \\ x^2=20^2+20^2 \\ x^2=400+400 \\ x^2=800 \\ x=\sqrt[]{800}=\sqrt[]{400*2} \\ x=20\sqrt[]{2}\text{ ft} \end{gathered}`

The length of the diagonal is 20√2 ft.