SOLUTION: A rectangle is 12 cm longer than it is wide. a wooden walk 2 ft wide is placed around the pond. the area covered by the pond and walk is 160 ft^2 greater than the area covered by t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A rectangle is 12 cm longer than it is wide. a wooden walk 2 ft wide is placed around the pond. the area covered by the pond and walk is 160 ft^2 greater than the area covered by t      Log On

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Question 984958: A rectangle is 12 cm longer than it is wide. a wooden walk 2 ft wide is placed around the pond. the area covered by the pond and walk is 160 ft^2 greater than the area covered by the pond alone. What are the dimensions of the pond
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Is the rectangle the same thing as the pond? Making sense of the description must permit these to be the same.

w width of pond
L length of pond
u the width of the WALK to surround the rectangular pond
-
L=w%2B12%2Acm%2A%281%2F2.54%29%28inch%2Fcm%29%281%2F12%29%28foot%2Finch%29
L=w%2B12%2F%282.54%2A12%29
L=w%2B1%2F2.54
L=w%2B0.3937008------decimal approximation;
Are you sure that part of the description is 12 CENTIMETERS longer?
-
A area of walkway alone;
A=160 ft^2
u=2

Total Area Pond Plus Walkway, %28w%2B2u%29%28L%2B2u%29
Area just the pond, wL
Just WALK area, highlight_green%28%28w%2B2u%29%28L%2B2u%29-wL=A%29

Start simplifying that last equation difference being A.
wL%2B2uL%2B2uw%2B4u%5E2-wL=A
2u%28L%2Bw%29%2B4u%5E2=A
2u%28L%2Bw%29=A-4u%5E2
highlight_green%28L%2Bw=%28A-4u%5E2%29%2F%282u%29%29, not yet finished symbolically...
You need to be sure about the description relating w and L, and when you are, you can readjust if necessary, and then continue, solving first ... for w.

If you meant what you described, then
%28w%2B0.3937008%29%2Bw=%28A-4u%5E2%29%2F%282u%29
2w=%28A-4u%5E2%29%2F%282u%29-0.3937008
highlight_green%28w=%28A-4u%5E2%29%2F%284u%29-0.19685%29, and just substitute the values to evaluate...

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle is 12 cm longer than it is wide. a wooden walk 2 ft wide is placed around the pond. the area covered by the pond and walk is 160 ft^2 greater than the area covered by the pond alone. What are the dimensions of the pond

Why the different measurements: cm and ft. Is this a RECTANGULAR pond? Couldn't you take some time to present the problem better than this?

Dimensions of the pond could be: highlight_green%28system%2812_ft_by%2C24_ft%29%29