Question

The length of a rectangle is $3$ times its width. If the area of the rectangle is $192{\mathrm{in}}^2$, how do you find its perimeter?

Answer 1

Step-1: Find the length and width of rectangle:

Let the width be $x$ And therefore the length becomes $3x$

Therefore, The area of rectangle becomes,

$$\begin{gathered} 3x^2=192 \\ \Rightarrow x^2=64 \\ \Rightarrow x=\pm 8 \end{gathered}$$

As width cannot be negative we have, $x=8\text{in}$

And hence the length of the rectangle is

$$\begin{gathered} \mathrm{length}=3\mathrm{x} \\ \mathrm{length}=3\left(8\right) \\ \mathrm{length}=24\mathrm{in} \end{gathered}$$

Step- 2: Find the perimeter of the rectangle:

The perimeter of the rectangle can be given by the formula

$\mathrm{P}=2(\mathrm{length}+\mathrm{width})$

Substituting the values we get,

$$\begin{gathered} \mathrm{P}=2(\mathrm{length}+\mathrm{width}) \\ \mathrm{P}=2(24+8) \\ \mathrm{P}=64\mathrm{in} \end{gathered}$$

Therefore, The perimeter of the rectangle is $\mathbf{64}\mathbf{in}\mathbf{.}$