SOLUTION: A rectangle is 5cm longer than its wide. If the length and breadth are increased by 2cm each, the area increases by 50cm2. FInd the dimensions of the original rectangle

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Question 826437: A rectangle is 5cm longer than its wide. If the length and breadth are increased by 2cm each, the area increases by 50cm2. FInd the dimensions of the original rectangle
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x length
w wide
w=x%2B5;
If x+2 and w+2, then area is increased, +50 cm*cm.

xw=A, A for area.
%28x%2B2%29%28w%2B2%29=A%2B50;
w=x%2B5.
'
Let us substitute for w into the two area equations.
x%28x%2B5%29=A,
highlight_green%28x%5E2%2B5x=A%29.----Original area
'
%28x%2B2%29%28%28x%2B5%29%2B2%29=A%2B50-----for Increased dimensions area
%28x%2B2%29%28x%2B7%29=A%2B50
x%5E2%2B9x%2B14=A%2B50, and remember we can also substitute for A;
x%5E2%2B9x%2B14=%28x%5E2%2B5x%29%2B50
x%5E2%2B9x%2B0=x%5E2%2B5x%2B36
9x=5x%2B36
4x=36
highlight%28x=9%29
-
Now to find value of w:
w=x%2B5
w=9%2B5
highlight%28w=14%29