Question

A grassy space is 6 feet by 8 feet. The town wants to add a walking track around this space. If the total area is to be 71 square feet, what

should be added to each side of the grassy space? (Round to the nearest hundredth.)

Answer 1

0.74 feet should be added to each side of the grassy space.

Explanation:

Let

x -----> the width of the walking track around the space

we know that

The total area is equal to

`A=(6+2x)(8+2x)`

`A=71\ ft^(2)`

so

`(6+2x)(8+2x)=71\\48+12x+16x+4x^(2)=71\\4x^(2)+28x+48-71=0\\4x^(2)+28x-23=0`

Solve the quadratic equation by graphing

The solution is x=0.743 ft

see the attached figure

therefore

0.74 feet should be added to each side of the grassy space.