Question

I need help finding the exact perimeter. Special right triangles.

Answer 1

The exact perimeter of the square is;

`56\sqrt[]{2}`

Step-by-step explanation:

Given the square in the attached image.

The length of the diagonal is;

`d=28`

Let l represent the length of the sides;

`\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=(784)/(2) \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}`

The perimeter of a square can be calculated as;

`\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}`

Therefore, the exact perimeter of the square is;

`56\sqrt[]{2}`