SOLUTION: The length of a rectangle exceeds its breadth by 7 ems. If the length is decreased by 4 cm. and the breadth is increased by 3 cms., then the area of the new rectangle will be the s

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle exceeds its breadth by 7 ems. If the length is decreased by 4 cm. and the breadth is increased by 3 cms., then the area of the new rectangle will be the s      Log On


   

Question 813515: The length of a rectangle exceeds its breadth by 7 ems. If the length is decreased by 4 cm. and the breadth is increased by 3 cms., then the area of the new rectangle will be the same as the area of the original rectangle. What will be the perimeter of the original rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x length, y breadth.
x=y+7.
Area initially is xy=x%28x-7%29. Perimeter would be 2x%2B2%28x-7%29=2x%2B2x-14=4x-14.

New situation.
x-4, length, and y+3, breadth. Remember, x=y+7 and means y=x-7.
Area now .
Perimeter now is 2%28x-4%29%2B2%28x-7%2B3%29=2x-8%2B2x-8=4x-16.

AREA OF NEW AND INITIAL ARE EQUAL.----Given.
x%28x-7%29=x%5E2-8x%2B16
x%5E2-7x=x%5E2-8x%2B16
-7x=-8x%2B16
highlight%28x=16%29
That means highlight%28y=9%29.

Question asked was, original perimeter.
2%2A16%2B2%2A9=32%2B18=highlight%2850%29 cms.