Answer:
A = 135m²
Step-by-step explanation:
- Represent the problem with equations
- Recall the formula for perimeter
- Find the dimensions of the rectangle (length and width)
- Recall the formula for area
- 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.
