Question

A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of the square garden.12 ft24 ft17 ft21 ft

Answer 1

Step 1: draw the diagram

The perimeter of a square is 4L

`\begin{gathered} \text{peremeter}=4L \\ 48=4l \\ l=(48)/(4) \\ l=12 \end{gathered}`

The diagonal of the square is hypotenuse side represented by D

Using Pythagoras theorem, we have

`\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ D^2=L^2+L^2 \end{gathered}`
`\begin{gathered} D^2=12^2+12^2 \\ =144+144 \\ =288 \\ D=\sqrt[\square]{288} \\ D=16.97 \end{gathered}`

Hence the approximate length of the diagonal is 17ft