SOLUTION: The area of a rectangular region is 104 square feet. If the length of the rectangle is increased by 4 feet and the width by 2 feet, then the area is increased by 66 square feet. Fi

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Question 900153: The area of a rectangular region is 104 square feet. If the length of the rectangle is increased by 4 feet and the width by 2 feet, then the area is increased by 66 square feet. Find the length and width of the original rectangular region.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L for width and length;
wL=104 for original rectangle.

%28L%2B4%29%28w%2B2%29-wL=66, think about the description as worded and how it is transcribable into this equation.
Lw%2B4w%2B2L%2B8-wL=66
wL-wL%2B4w%2B2L=66
4w%2B2L=66
2w%2BL=33
Might be easiest to use this as L=33-2w and substitute into original area equation:
wL=104
w%2833-2w%29=104
-2w%5E2%2B33w-104=0
highlight_green%282w%5E2-33w%2B104=0%29
Avoid trying to factorize, using general solution of a quadratic equation.
Discriminant,33^2-4*2*104=257
highlight%28w=%2833%2Bsqrt%28257%29%29%2F4%29
and
L=104%2Fw
L=104%284%2F%2833%2Bsqrt%28257%29%29%29
highlight%28L=416%2F%2833%2Bsqrt%28257%29%29%29