# The length of a rectangle is 3 times its width. If the area of the rectangle is "192 in"^2, how do you find its perimeter?

Mar 16, 2018

The perimeter is $64$ inches

#### Explanation:

First find the lengths of the sides of the rectangle

Use the information about $a r e a$ to find the lengths of the sides.

Begin by finding a way to describe each side using math language.

Let $x$ represent the width of the rectangle

Width . . . . . . . . . $x$ $\leftarrow$ width
$3$ times that . . . $3 x$ $\leftarrow$ length

The area is the product of these two sides
[ width ] $\times$ [ length ] $=$ Area
[ . . $x$. . .] $\times$ [ . . $3 x$ . .]  =  192

$192 = \left(x\right) \left(3 x\right)$   Solve for $x$, already defined as the width

1) Clear the parentheses by distributing the $x$
192 = 3 x^2

2) Divide both sides by $3$ to isolate ${x}^{2}$
$64 = {x}^{2}$

3) Take the square roots of both sides
$\sqrt{64} = {\sqrt{x}}^{2}$

$\pm 8 = x$, already defined as the width of the rectangle

The width cannot be a negative number, so $- 8$ is a discarded solution.

The width of the rectangle is $8$ inches
So the length must be $3 \times 8$, which is $24$ inches.

Now use the lengths of the sides of the rectangle to find its perimeter

Perimeter is the sum of all four sides

[ $2$ widths ] + [  2 lengths ]$=$ Perimeter
[... ..2(8) ...] + [ ..2(24)..] = Perimeter

1) Clear the parentheses
$16 + 48 =$ Perimeter

$64 =$ Perimeter
1) The sides should multiply up to an area of 192  "in"^2
$8 \times 24 = 192$
$C h e c k$