Chapter 4.3, Problem 47PPS

To determine

To calculate: The value of x and dimensions of rectangle.

  

Answer to Problem 47PPS

The value of x is $20$ and dimensions of the rectangle are $24\text{ in}\text{. by 18 in}\text{.}$ .

Explanation of Solution

Given information:

The figure,

  

Formula used:

Area of a rectangle with length l and breadth b is the product of its length and breadth.

  $\text{A}=l\times b$

Calculation:

Consider the given figure,

  

In the above figure, $l=x+4\text{ in}\text{.}$ , $b=x-2\text{ in}\text{.}$ and area is $432{\text{ in}}^2$ .

Recall that area of a rectangle with length l and breadth b is the product of its length and breadth.

  $\text{A}=l\times b$

Apply it,

  $\begin{array}{c}432=\left(x+4\right)\left(x-2\right)\\ x^2-2x+4x-8=432\\ x^2+2x-440=0\\ \left(x+22\right)\left(x-20\right)=0\end{array}$ .

Since, side cannot be negative, hence, $x=20$ .

Now, length and breadth of the rectangle is calculated as,

  $\begin{array}{c}l=x+4\\ =20+4\\ =24\text{ in}\text{.}\end{array}$

  $\begin{array}{c}b=x-2\\ =20-2\\ =18\text{ in}\text{.}\end{array}$

Thus, the value of x is $20$ and dimensions of the rectangle are $24\text{ in}\text{. by 18 in}\text{.}$ .