The combined area of a square and a rectangle is 116 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width. Find the dimensions of the square and the rectangle.
A) 6 centimeters by 6 centimeters and 8 centimeters by 8 centimeters
B) 6 centimeters by 6 centimeters and 8 centimeters by 10 centimeters
C) 8 centimeters by 8 centimeters and 6 centimeters by 8 centimeters

Question

Quizplus · Accepted Answer

Let x be the length of a side of the square. Then the width of the rectangle is x + 2 and the length of the rectangle is (x + 2) + 2 = x + 4. The combined area of the square and rectangle is x^2 + (x + 2)(x + 4) = 116. Simplifying this equation gives x^2 + 6x - 104 = 0, which can be factored as (x + 13)(x - 8) = 0. Since the length of a side of a square cannot be negative, x = 8 is the only solution. Therefore, the dimensions of the square are 8cm by 8cm, and the dimensions of the rectangle are 8cm + 2cm by 8cm + 4cm, or 10cm by 12cm. Thus, the answer is B.

The Combined Area of a Square and a Rectangle Is