Question

The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 48 m, find its area.

Answer 1

135m^2

Explanation:

length = l

width = w

l + l + w + w = 48

l = w+6

w+6 + w+6 + w + w = 48

4w + 12=48

4w=36

w=9

l=15

15*9=135

Answer 2

A = 135m²

Explanation:

1. Represent the problem with equations
2. Recall the formula for perimeter
3. Find the dimensions of the rectangle (length and width)
4. Recall the formula for area
5. Use the dimensions to find the area

Write equations to represent the problem.

l = w + (6m) The length is 6m more than the width

P = (48m) Perimeter is 48m

***We put brackets around numbers with the "m" to avoid confusing the units with a variable.

The formula for perimeter of a rectangle is P = 2(l + w)

Substitute "l" and "P" into the perimeter formula with the equations above. Simplify, then isolate "w".

P = 2(l + w)

(48m) = 2(w + (6m) + w) Collect like terms (w + w = 2w)

(48m) = 2(2w + (6m)) Distribute over brackets

(48m) = 4w + (12m) Start isolating "w"

(48m) - (12m) = 4w + (12m) - (12m) Subtract 12m from both sides

(36m) = 4w

4w/4 = (36m)/4 Divide both sides by 4

w = 9m Width of rectangle

Find "l" using the formula for length. Substitute the width.

l = w + (6m)

l = (9m) + (6m) Add

l = 15m Length of rectangle

Use the formula for the area of a rectangle A = lw.

Substitute the values we found for length and width.

A = lw

A = (15m)(9m) Multiply

A = 135m² Area of rectangle

Therefore the area of the rectangle is 135m².