Chapter 5.7, Problem 19PSB

To determine

Tofind: the perimeter of given rectangle.

Answer to Problem 19PSB

Perimeter of the given rectangle is, $P=52\text{ units}$

Explanation of Solution

Given information:

In rectangle,

Length $\left(l\right)=x+6\text{ units}$

Breadth $\left(b\right)=x\text{ units}$

Area $\left(A\right)=160{\text{ units}}^2$

Formula used:

Perimeter of the rectangle is, $P=2\times l\times b\text{ units}$

Calculation:

Let the rectangle be $ABCD$

  $\begin{array}{l}\text{Given }A=160\\ \Rightarrow l\times b=160\left[\because \text{ Area of rectangle = }l\times b\right]\\ \Rightarrow \left(x+6\right)\times x=160\\ \Rightarrow x^2+6x=160\\ \Rightarrow x^2+6x-160=0\\ \Rightarrow x^2+16x-10x-160=0\\ \Rightarrow x\left(x+16\right)-10\left(x+16\right)=0\\ \Rightarrow \left(x-10\right)\left(x+16\right)=0\\ \Rightarrow x=10\text{ or }x=-16\end{array}$

Since, measurement can’t be negative, $x\ne -16$

Hence $x=10$

Now, perimeter of the rectangle is,

  $\begin{array}{l}P=2\times \left(l+b\right)\\ =2\times \left(x+x+6\right)\\ =2\times \left(2x+6\right)\\ =2\times \left(2\times 10+6\right)\\ =2\times \left(20+6\right)\\ =2\times 26\\ =52\text{ units}\end{array}$