Question

The length of a rectangle is (5x − 1) cm and the width is (11 − 2x) cm. If the perimeter of the rectangle is 44 centimeters, what is the area of the rectangle?

Answer 1

Answer:

57 cm²

Step-by-step explanation

l = length

w = width

p = perimeter

(5x - 1) = length

(11 - 2x) = width

44 = perimeter

Formula for the perimeter of a rectangle:

l + l + w + w

2l + 2w = p

Substitute the variables for the length and width with the values given to you by the problem, then solve.

2(5x - 1) + 2(11 - 2x) = 44

(10x - 2) + (22 - 4x) = 44 (Distributive property)

6x + 20 = 44

6x = 24

x = 4

Plug x = 4 back into the length and width.

Length = (5x - 1), (5(4) - 1), (19)

Width =  (11 - 2x), (11 - 2(4)), (3)

Area for a rectangle: Length × Width = Area.

19 × 3 = 57 cm²

This is all in cm so answer with cm²