The combined area of a square and a rectangle is 102 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 4 centimeters more than its width. Find the dimensions of the square and the rectangle.
A)5 centimeters by 7 centimeters and 11 centimeters by 11 centimeters
B)7 centimeters by 7 centimeters and 5 centimeters by 9 centimeters
C)5 centimeters by 5 centimeters and 7 centimeters by 11 centimeters
D)5 centimeters by 5 centimeters and 7 centimeters by 9 centimeters
E)none of these

Question

Quizplus · Accepted Answer

Let the side of the square be $x$ cm. Then, the width of the rectangle is $x + 2$ cm, and its length is $x + 2 + 4 = x + 6$ cm. The total area is given by $x^2 + (x + 2)(x + 6) = 102$. Solving this equation, we find $x = 5$, so the square's side is 5 cm, making the rectangle's dimensions 7 cm by 11 cm.

The Combined Area of a Square and a Rectangle Is