Solve the problem.
-The side of a square equals the width of a given rectangle. The length of the rectangle is 4 centimeters greater than its width. The sum of the areas of the square and the rectangle is 126 square centimeters. Find the side of
The square.
A) 49 cm
B) 9 cm
C) 7 cm
D) 2 cm

Question

Quizplus · Accepted Answer

Let x be the width of the rectangle. Then the length of the rectangle is x + 4.
The area of the square is x^2.
The area of the rectangle is x(x + 4) = x^2 + 4x.
The sum of the areas of the square and the rectangle is x^2 + x^2 + 4x = 126.
Simplifying this equation, we get 2x^2 + 4x - 126 = 0.
Dividing both sides by 2, we get x^2 + 2x - 63 = 0.
Factoring this equation, we get (x + 9)(x - 7) = 0.
Therefore, x = -9 or x = 7. Since x represents a length, we take x = 7 as the valid solution.
The side of the square equals the width of the rectangle, which is 7 cm. Let x be the width of the rectangle. Then, the length of the rectangle is x + 4. 
The area of the square is x^2. 
The area of the rectangle is x(x + 4) = x^2 + 4x. 
The sum of the areas is x^2 + (x^2 + 4x) = 2x^2 + 4x. 
We are given that the sum of the areas is 126, so 2x^2 + 4x = 126. 
Simplifying, we get x^2 + 2x - 63 = 0. 
Factoring, we get (x + 9)(x - 7) = 0. 
Since the width of the rectangle cannot be negative, we have x = 7. 
Therefore, the side of the square is also 7 cm.

Solve the Problem. -The Side of a Square Equals the Width of a Width