SOLUTION: If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that o

Question 505171: If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square.
Find the dimensions of the rectangle?
:
let x = the side of the square
then
x^2 = the area of the square
:
2x = length of the rectangle
(x-2) = width of the rectangle
then
2x(x-2) = 2x^2 - 4x = the area of the rectangle
:
Rect area - square area = 96 sq/cm
2x^2 - 4x - x^2 = 96
Forms a quadratic equation
x^2 - 4x - 96 = 0
factors to
(x-12)(x+8) = 0
positive solution
x = 12 cm is the side of the square
then
2(12) = 24 cm is the length of the rect
and
12-2 = 10 cm is the width of the rect
;
:
:
Check this
24*10 - 12^2 =
240 - 144 = 96 sq/cm difference
RELATED QUESTIONS
if the length of one side of a square is doubled and the length of an adjacent side is... (answered by ankor@dixie-net.com)

If each side of a square is decreased by 5 centimeters, its area will decrease by 175... (answered by josgarithmetic)

if one side of a square is increased by 3 inches and the adjacent side is decreased by 2... (answered by ankor@dixie-net.com)

If one side of a square is increased by 2 inches and an adjacent side is decreased by 2... (answered by checkley77)

If one side of a square is increased by 4 feet and an adjacent side is decreased by two... (answered by ankor@dixie-net.com)

if two opposite side of a square are each increased by 3centimeters, and the other sides... (answered by mananth)

If one side of a square is increased by 8 cm and an adjacent side is decreased by 2 cm, a (answered by jrfrunner)

if one side of a square is increased by 8 feet and an adjacent side is decreased by 2... (answered by jorel1380,htmentor)

If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a... (answered by J2R2R)