Chapter 4.9, Problem 1OE

To determine

To calculate: the original dimension of rectangle.

Answer to Problem 1OE

Length = 11 cm & width = 6 cm

Explanation of Solution

Given:

Length of the rectangle increased by 5 cm

Length & width increased by 3cm

Area increased by 60 cm²

Calculation:

Let width of the original rectangle be = $x$ cm

Let length of the original rectangle be = $x+5$ cm

Now area of the original rectangle = $x\left(x+5\right)$ cm²

Length & width increased by 3 cm

So, length of the new rectangle = $\left(x+5\right)+3=\left(x+8\right)$ cm

length of the new rectangle = $\left(x+3\right)$ cm

area of new rectangle = $\left(x+8\right)\left(x+3\right)$ cm²

area of new rectangle increased by 60 cm²

now subtracting original area from new area

  $\begin{array}{l}\left(x+8\right)\left(x+3\right)-x\left(x+5\right)=60\\ x^2+3x+8x+24-x^2-5x=60\\ 6x+24=60\\ 6x=60-24\\ 6x=36\\ x=\frac{36}{6}\\ x=6\end{array}$

So, width of the original rectangle is 6 cm

Length of the original rectangle

  $\begin{array}{l}x+5\\ 6+5=11\text{ cm}\end{array}$