Question

Two opposite sides of a square with length x are increased by 3 units each and the other two opposite sides are decreased by 3 units each. If the area of the resulting rectangle is 27 unit^2, what would be the width of the rectangle? Hint: area of rectangle = length × width

A 3
B 6
C 9
D -3
E -6

Answer 1

All four sides of the original square have length s.

Adding 3 to s results in s+3, the length of the resulting rectangle.
Subtracting 3 from s results in s-3, the width of the rectangle.

The area of the rectangle is (s+3)(s-3) = s^2 - 9 = 27,

and therefore s^2 = 36, and s = 6 square units.