Question

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

Answer 1

Hint: From the question we get the length of a rectangle is $3$ times its width and the area is given. First we determine the length and width of the rectangle. After that use the formula of area of a rectangle i.e., ${\text{Area = Length}} \times {\text{Width}}$ of the rectangle and equate to the given value of area of rectangle and we get the value of width and find the actual length of the rectangle. After that we find the perimeter of the rectangle by using the formula of perimeter of the rectangle i.e., ${\text{Perimeter = 2(Length + Width)}}$ of the rectangle and we get the required answer.

Complete step by step answer:
Given that the length of a rectangle is $3$ times its width.
Let the width be $x$ in.
Therefore the length of the rectangle is $3x$ in.
We find the area of the rectangle by using the formula ${\text{Area = Length}} \times {\text{Width}}$
Here Length $ = 3x$ in and width $ = x$ in.
Put this in the above formula and we get
Area $ = 3x \times x$
$ = 3{x^2}{\text{i}}{{\text{n}}^2}$
In the problem given that the area of the rectangle $192{\text{ i}}{{\text{n}}^2}$
Therefore equate them and we get
$3{x^2} = 192$
Divide both sides by $3$ and we get
$ \Rightarrow {x^2} = \dfrac{{192}}{3}$
Simplifying the above equation and we get
$ \Rightarrow {x^2} = 64$
Take square root both sides and we get
$ \Rightarrow \sqrt {{x^2}} = \sqrt {64} $
$ \Rightarrow x = 8$
Therefore the width is $8$ in.
The length of the rectangle is $3 \times 8$ in
$ = 24$ in.
Now we find the perimeter of the rectangle by using the formula of perimeter of the rectangle i.e., ${\text{Perimeter = 2(Length + Width)}}$
Therefore perimeter $ = 2(24 + 8)$ in
$ = 2 \times 32$
$ = 64$ in.
Therefore the perimeter of the rectangle is $64$ in.

Note:
 To solve this type of problem students must remember the formulas of the rectangle. Must remember the formulas of perimeter, area and diagonal of the rectangle. When we take square root then we must take the positive values because negative values are not accepted for the values of perimeter and area of a rectangle. So always take positive signs only.