SOLUTION: If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased by 4cm and the breadth is increased by 3cm,The original rectangle area is equal to the new

Algebra ->  Rectangles -> SOLUTION: If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased by 4cm and the breadth is increased by 3cm,The original rectangle area is equal to the new       Log On


   

Question 890289: If the length of the rectangle is exceeds its breadth by 7cm and the length is decreased by 4cm and the breadth is increased by 3cm,The original rectangle area is equal to the new rectangle area,Find its perimeter?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L for original rectangle.
L-w=7 for this original rectangle.
L=w+7.
area is wL.
area is w(w+7).

New rectangle.
L-4 and w+3 become new length and breadth.
area is (L-4)(w+3).
This area again using the expression for L as earlier, is (w+7-4)(w+3),
which is (w+3)(w+3), the "new" area.

These areas were given as EQUAL.
w%28w%2B7%29=%28w%2B3%29%5E3
Simplify and solve for w.
w%5E2%2B7w=w%5E2%2B6w%2B9
7w=6w%2B9
highlight%28w=9%29
Compute L from the earlier described formula.
L=w%2B7
L=9%2B7
highlight%28L=16%29
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Now you can calculate the perimeter of the original rectangle because you know the values for w and L.
p=2w%2B2L
p=2*9+2*16
p=18+32
p=50----------------the answer