Chapter 4.8, Problem 13P

To determine

To find the dimensions of the new rectangle.

Answer to Problem 13P

The dimensions of new rectangle is and $14cm$ and $11cm$ .

Explanation of Solution

Given information: A rectangle is $15cm$ wide and $18cm$ long. Area of new rectangle formed is $116c{m}^2$ less than the area of the original.

Calculation: The dimensions of new rectangle is obtained as,

Let, $18-x$ be length of new rectangle,

And $15-x$ be wide of new rectangle.

Area of smaller rectangle equals original area minus $116$ .

  $\begin{array}{l}\left(18-x\right)\left(15-x\right)=\left(18\right)\left(15\right)-116\\ 270-18x-15x+x^2=270-116\\ x^2-33x+270=154\\ x^2-33x+116=0\\ \left(x-29\right)\left(x-4\right)=0\\ x=29,4\end{array}$

Take $x=4$ ,

29 is not valid since the smaller rectangle wouldn’t be possible.

  $18-x=18-4=14$ is length

  $15-x=15-4=11$ is wide

Hence, the dimensions of new rectangle is and $14cm$ and $11cm$ .