Solve.
-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)12 cm
B)9 cm
C)3 cm
D)4 cm

Question

Quizplus · Accepted Answer

Let x be the side length of the square. Then we have:
x^2 = 81  (since the area of square is given as 81 sq cm)
x = 9   (taking square root both sides, as x is positive)
Now, if we add 3 cm to one dimension and subtract 3 cm from the other dimension of the square, we get a rectangle with length (9+3) = 12 cm and width (9-3) = 6 cm. 
The area of this rectangle is (12*6) = 72 sq cm. 
According to the given condition, this area is 9 sq cm less than the area of the square. So we have:
x^2 - (12*6) = 9
9^2 - (12*6) = 9
81 - 72 = 9
Therefore, the correct answer is C) 3 cm.

Solve. -The Area of a Square Is 81 Square Centimeters. If