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

Answer:

The width of the walkway is 4 feet.

Step-by-step 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.

$(12+2x)\times(15+2x)= 460$

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 = $-\frac{35}{2}$

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

Hence, the width of the walkway is 4 feet.