Solve the problem.
-The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is added and subtracted?
A) $4 \mathrm{~cm}$
B) $3 \mathrm{~cm}$
C) $9 \mathrm{~cm}$
D) $12 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The side of the square is 9 cm (since $9^2 = 81$). Let $x$ be the amount added and subtracted. The new dimensions are $9 + x$ and $9 - x$. The area of the rectangle is $(9 + x)(9 - x) = 81 - x^2$. We know this area is 9 cm² less than the square's area, so $81 - x^2 = 72$. Solving for $x$, we get $x^2 = 9$, so $x = 3$.

Solve the Problem 4 cm4 \mathrm{~cm}4 cm B) 3 cm3 \mathrm{~cm}3 cm C) 9 cm9 \mathrm{~cm}9 cm D) 12 cm12 \mathrm{~cm}12 cm

Solve the Problem $4 \mathrm{~cm}$ B) $3 \mathrm{~cm}$ C) $9 \mathrm{~cm}$ D) $12 \mathrm{~cm}$