Chapter 7.2, Problem 2P

To determine

To find: The value of x .

Answer to Problem 2P

The value of x is 4 cm.

Explanation of Solution

Given:

The length of the rectangle = 6 cm.

The width of the rectangle = 5cm

Calculation:

The area of the rectangle is given by

  $\begin{array}{l}A=l\times b\\ \text{Here, }l\text{is the length of the rectangle and }b\text{ is the bredth of the rectangle}\text{.}\end{array}$

The initial area of the rectangle

  $\begin{array}{l}{A}_1=5\times 6\\ A_1=30{\text{ cm}}^2\end{array}$

Each side of the rectangle is increased by x m. The area becomes triple.

New area of the rectangle becomes

  $\begin{array}{l}{A}_2=\left(5+x\right)\times \left(6+x\right)\\ A_2=3A_1\\ 3\times 30=\left(5+x\right)\times \left(6+x\right)\\ 30+11x+x^2=90\\ x^2+11x-60=0\\ x^2+15x-4x-60=0\\ x\left(x+15\right)-4\left(x+15\right)=0\\ \left(x-4\right)\left(x+15\right)=0\\ x=4\\ x=-15\end{array}$

The dimension of the rectangle cannot be negative. The value of x is 4.

Therefore, the value of x is 4 cm.

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