Question

A rectangular pool 18 meters by 12 meters is surrounded by a walkway of width x

meters. At what value of x will the area of the walkway equal the area of the pool?

Answer 1

3

Explanation:

Answer 2

x=3 meters

Explanation:

step 1

Find the area of the rectangular pool

`A=LW`

we have

`L=18\ m\\W=12\ m`

substitute

`A=18(12)=216\ m^2`

step 2

Find the area of rectangular pool including the area of the walkway

Let

x ----> the width of the walkway

we have

`L=(18+2x)\ m\\W=(12+2x)\ m`

substitute

`A=(18+2x)(12+2x)`

step 3

Find the area of the walkway

To find out the area of the walkway subtract the area of the pool from the area of rectangular pool including the area of the walkway

so

`A=(18+2x)(12+2x)-216`

step 4

Find the value of x if the area of the walkway equal the area of the pool

so

`(18+2x)(12+2x)-216=216`

Solve for x

`(18+2x)(12+2x)=432\\216+36x+24x+4x^(2)=432\\4x^(2) +60x-216=0`

Solve the quadratic equation by graphing

The solution is x=3 meters

see the attached figure