Question

61. A square garden has a 4-ft walkway around it. The gardenhas a perimeter of 260 ft. What is the area of the walkway insquare feet?

Answer 1

Consider the following diagram,

Let 'y' be the side of the garden. And 'x' be the side of the square formed by the walkway.

Given that the garden is a square with perimeter 260 feet,

`\begin{gathered} \text{Perimeter}=260 \\ 4y=260 \\ y=65 \end{gathered}`

From the above diagram, it can be observed that,

`\begin{gathered} x=4+y+4 \\ x=8+y \\ x=8+65 \\ x=73 \end{gathered}`

Consider that the area of a square is given by,

`\text{Area of square}=Side^2`

The area of the inner square i.e. garden will be,

`\begin{gathered} A_i=y^2 \\ A_i=65^2 \\ A_i=4225 \end{gathered}`

The area of the outer square will be,

`\begin{gathered} A_o=x^2 \\ A_o=73^2 \\ A_o=5329 \end{gathered}`

The difference between the area will give the area of the walkway (A), that can be calculated as,

`\begin{gathered} A=A_o-A_i \\ A=5329-4225 \\ A=1104 \end{gathered}`

Thus, the area of the walkway is 1104 square feet.