Chapter 8, Problem 26MCQ

To determine

To Find: The Length of the rectangle.

Answer to Problem 26MCQ

The value of width is 6 inches and value of the rectangle is 8 inches.

Explanation of Solution

Given information:

Length of rectangle is $(2+x)$ inch.

Assume the width of rectangle is $x$ inches.

The length of the rectangle is 2 inches longer than its width. That is,

Length of rectangle is $(2+x)$ inch.

The area of the rectangle is 48 square inches.

The area of the rectangle is,

Area = Length * Width............(1)

Substitute the value of length equal to $(2+x)$ inch and width of rectangle is $x$ inches in equation (1) as,

  $48\text{ Square inches}=(2+x)(x)\text{ square inches}$

  $\begin{array}{l}48=(2+x)(x)\hfill \\ 48=2x+x^2\hfill \end{array}$

  $x^2+2x-48=0$ Subtract 48 from both sides

Solve the above equation as follows:

  $x^2+2x-48=0$

  $(x-6)(x+8)=0$ Factor

  $x-6=0$ or $x+8=0$ Zero Product Property

  $x=6x=-8$ solve each equation

Thus, the value of $x$ is either 6 or −8.

The length of the rectangle van never be negative and hence, the value of $x$ is 6.

Thus, the value of width is 6 inches and value of the rectangle is 8 inches.