Question

Jamie has a garden that is 20 meters by 30 meters. He wants to have a concrete pathway that is the same width all around the edge of the garden. If Jamie has enough concrete to cover 336 square meters, how wide will the pathway be?

Answer 1

3

Explanation:

Got 100

Answer 2

The pathway will be 3 meters wide

Explanation:

Let

x ----> the width of the pathway

we know that

The area of the pathway is equal to the area of the garden plus the pathway minus the area of the garden

The area of the pathway must be equal to 336 square meters

so

the linear equation that represent this situation is

`(2x+30)(2x+20)-(30)(20)=336`

solve for x

`4x^2+40x+60x+600-600=336`

`4x^2+100x=336`

`4x^2+100x-336=0`

Simplify the quadratic equation (Divide by 4 both sides)

`x^2+25x-84=0`

Solve the quadratic equation by graphing

using a graphing tool

The solution is x=3 m

see the attached figure

therefore

The pathway will be 3 meters wide