Solve.
-The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 198 square centimeters.
Find the side of the square.
A) 2 cm
B) 11 cm
C) 9 cm
D) 81 cm

Question

Quizplus · Accepted Answer

The side of the square (s) is equal to the length of the rectangle (l). The width of the rectangle (w) is l + 4. The areas combined give us $s^2 + l(w) = 198$. Substituting $w = l + 4$ and $s = l$, we get $l^2 + l(l + 4) = 198$. Simplifying, $2l^2 + 4l - 198 = 0$. Dividing everything by 2 gives $l^2 + 2l - 99 = 0$. Factoring, we find $l = 9$ or $l = -11$. Since a side length can't be negative, $l = 9$, so the side of the square is 9 cm.

Solve. -The Side of a Square Equals the Length of a a Rectangle