The length of a rectangle is 3 times its width. If the area of the rectangle is "192 in"^2192 in2, how do you find its perimeter?

1 Answer
Mar 16, 2018

The perimeter is 6464 inches

Explanation:

First find the lengths of the sides of the rectangle

Use the information about areaarea to find the lengths of the sides.

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

Let xx represent the width of the rectangle

Width . . . . . . . . . xx larr width
33 times that . . . 3x3x larr length

The area is the product of these two sides
[ width ] xx× [ length ] == Area
[ . . xx. . .] xx× [ . . 3x3x . .] =  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