The perimeter of a rectangle is 44 centimeters and the area is 112 square centimeters. Find the length and width of the rectangle.
A) 7 cm, 16 cm
B) 6 cm, 16 cm
C) 8 cm, 14 cm
D) 7 cm, 13 cm
E) 10 cm, 12 cm

Question

Quizplus · Accepted Answer

Let the length of the rectangle be L and let the width be W.

We know that the perimeter (P) of a rectangle is given by: 
P = 2L + 2W

And we know that the area (A) of a rectangle is given by: 
A = L * W

We are given that the perimeter is 44 cm, so we can write: 
2L + 2W = 44

Simplifying this equation, we get: 
L + W = 22

We are also given that the area is 112 cm^2, so we can write: 
L * W = 112

Now we can use substitution to solve for L and W. From the equation L + W = 22, we can write: 
L = 22 - W

Substituting this into the equation L * W = 112, we get: 
(22 - W) * W = 112

Expanding the left side, we get: 
22W - W^2 = 112

Rearranging and simplifying, we get a quadratic equation: 
W^2 - 22W + 112 = 0

We can solve this by factoring or using the quadratic formula. Factoring gives: 
(W - 8) (W - 14) = 0

So W = 8 or W = 14. If W = 8, then L = 22 - W = 14. If W = 14, then L = 22 - W = 8.

Therefore, the possible dimensions of the rectangle are: 
L = 8 cm, W = 14 cm 
or 
L = 14 cm, W = 8 cm

However, we are looking for the length and width of the rectangle, not just the possible dimensions. Therefore, the correct answer is: 
Choice C: 8 cm, 14 cm

The Perimeter of a Rectangle Is 44 Centimeters and the Area