Question

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?

Answer 1

The perimeter is `64` inches

Explanation:

First find the lengths of the sides of the rectangle

Use the information about `area` 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` `larr` width
`3` times that . . . `3x` `larr` length

The area is the product of these two sides
[ width ] `xx` [ length ] `=` Area
[ . . `x`. . .] `xx` [ . . `3x` . .] `=  192`

`192 = (x)(3x)`   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
`sqrt64 = sqrtx^2`

`+-8 = x`, already defined as the width of the rectangle

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

Answer:
The width of the rectangle is `8` inches
So the length must be `3xx8`, 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

2) Add
`64 =` Perimeter

Check

1) The sides should multiply up to an area of `192  "in"^2`
`8 xx 24 = 192`

`Check`