Chapter 4.8, Problem 14P

To determine

To find the dimensions of the original rectangle.

Answer to Problem 14P

The dimensions of original rectangle is and $8cm$ and $16cm$ .

Explanation of Solution

Given information: A rectangle is twice as long as it is wide. Its length is increased by 4cm and its width is decreased by 36cm, the new rectangle formed has an area of $100c{m}^2$ .

Calculation: The dimensions of original rectangle is obtained as,

For, Original rectangle,

Let, width be $x$ and length be $2x$ .

For, new rectangle,

Let, width be $x-3$ and length be $2x+4$ .

Area of new rectangle is $100c{m}^2$

  $\begin{array}{l}\left(x-3\right)\left(2x+4\right)=100\\ 2x^2-6x+4x-12=100\\ 2x^2-2x-112=0\\ x^2-x-56=0\\ \left(x+7\right)\left(x-8\right)=0\\ x=-7,8\end{array}$

Ignore negative value.

Original rectangle,

  $x=8$ is width.

  $2x=2\cdot 8=16$ is length.

Hence, the dimensions of original rectangle is and $8cm$ and $16cm$ .