The length of a rectangle is twice its width. If the perimeter of the rectangle is 36m What is the area?

2 Answers

Area = 72m^2

Explanation:

Perimeter of rectangle is 2l + 2w

now l=2 × w
l=2w

Perimeter = (2 × w) + (2 × 2w)
Perimeter = 2w+4w

36=6w

w=36/6

w=6

Hence, width = 6m.

Now Area of rectangle is l w

Since w=6m, length l = 2w = 2×6 = 12m

Area = 6 xx 12 = 72m^2

May 2, 2018

Area = 72 meters²

Explanation:

This problem is confusing for a couple of reasons.

For one thing, it's hard to know how to write a math expression for "The length of a rectangle is twice its width."

For another thing, it gives you information about perimeter, but it wants an answer about area.

The trick is to proceed one step at a time.

color(white)(mmmmmmmm)―――――――――

Step 1:
Mathematically express the relationships among the dimensions.

Let x represent the number of meters in the width.

Width . . . . . . . . . . . . . . . x larr number of meters in the width
Twice this amount . . . 2x larr number of meters in the length

[ Two widths ] plus [ two lengths ] equals the perimeter
color(white)    2 (x) color(white)(mn  ] + color(white)(.)[     2 (2x)color(white)(nn ]   =        36 m

2x + 2(2x) = 36

color(white)(mmmmmmmm)―――――――――

Step 2:
Solve for x

x is already defined as "the number of meters in the width"

2x + 2(2x) = 36

1) Clear the parentheses by distributing the 2
2x + 4x = 36

2) Combine like terms
6x = 36

3) Divide both sides by 6 to isolate x, already defined as "the number of meters in the width"
x = 6 larr the number of meters in the width

So the length, which is given as "twice as long," must be 12

color(white)(mmmmmmmm)―――――――――

Step 3:
Use the dimensions of the rectangle to find its area

Area  is  width× length
A      =   6m  ×   12m

Area = 72  meters² larr answer