Chapter 9.4, Problem 24P

Ling is cutting carpet for a rectangular room. The area of the room is 324 $f{t}^2$.

The length of the room is 3 feet longer than twice the width. What should the dimensions of the carpet be?

To determine

To calculate: In case the question requires us to calculate the dimension of the carpet.

Answer to Problem 24P

The width of the carpet is $y=12$ feet and length of the carpet is $x=27$ feet

Explanation of Solution

Given information: Consider the given information,

Area of the room is $324f{t}^2$

Length of the room be x and width be y

Therefore, the length of the room’s equation be $x=2y+3$

Calculation : the solution for the following equation will be,

  $x=2y+3$

  $xy=324$

  $(2y+3)y=324$

  $2y^2+3y=324$

  $2y^2+3y-324=0$

  $2y^2+27y-24y-324=0$

  $y(2y+27)-12(2y+27)=0$

  $(2y+27)(y-12)=0$

  $2y+27=0$

  $2y=-27$

  $y\ne -\frac{27}{2}$

And $y-12=0$

So $y=12$

Therefore, the width of the carpet is $y=12$ and length of the carpet is $x=2\times y+3$

  $x=2\times 12+3=27$