SOLUTION: A rectangle having twice the area of a square is formed by decreasing two parallel sides of the square by 2 cm. and increasing the other two parallel sides by 12 cm. How long is ea

Algebra ->  Rectangles -> SOLUTION: A rectangle having twice the area of a square is formed by decreasing two parallel sides of the square by 2 cm. and increasing the other two parallel sides by 12 cm. How long is ea      Log On


   

Question 155022: A rectangle having twice the area of a square is formed by decreasing two parallel sides of the square by 2 cm. and increasing the other two parallel sides by 12 cm. How long is each side of the square?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Area%5BR%5D=2%2AArea%5BS%5D ---------------> working eqn
To satisfy the ABOVE condition ----> decreasing 2 parallel sides by 2cm and increasing the other by 12cm to formed the Area of the rectangle:
Remember: For the Square, sides=s
For the Rectangle, Width=s-2cm, & Lenght=s%2B12cm
Therefore, going back working eqn
%28s-2%29%28s%2B12%29=2%2A%28s%5E2%29 ----------------------> eqn 1
s%5E2-2s%2B12s-24=2s%5E2
2s%5Es-s%5E2%2B2s-12s%2B24=0
s%5E2-10s%2B24=0, perfect square
%28s-6%29%28s-4%29=0
2 values:system%28s=6cm%2Cs=4cm%29
SO THE SIDES OF THE SQUARE COULD BE 6CM OR 4CM. TO CHECK, SIMPLY SUBSTITUTE EITHER S=6CM OR 4CM TO EQN 1.
Thank you,
Jojo