Question

A vacant lot is being converted into a community garden. The garden and and a walkway around its perimeter have an area of 460 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.

Answer 1

The width of the walkway is 4 feet.

Explanation:

The garden and a walkway around its perimeter have an area of 460 square feet.

The length of the garden = 15 feet

The width of the garden = 12 feet

Assuming that walkway is of uniform width, we can solve the following equation.

`(12+2x)*(15+2x)= 460`

Expanding this we get;

`4x^(2)+54x+180=460`

`=> 4x^(2)+54x-280=0`

We will solve this using quadratic equation formula:

`x=\frac{-b\pm \sqrt{b^(2) -4ac} }{2a}`

Here a = 4 , b = 54 , c = -280

We get the roots as x = 4 and x =
`-(35)/(2)`

Neglecting the negative value, we will take x = 4 feet.

Hence, the width of the walkway is 4 feet.