SOLUTION: A childrens park is 3500m long and 200m wide. It is sorrounded by a pathway of uniform width. Suppose the total area of the park and the pathway is 74,464mē. How wide is the pathwa

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Question 988221: A childrens park is 3500m long and 200m wide. It is sorrounded by a pathway of uniform width. Suppose the total area of the park and the pathway is 74,464mē. How wide is the pathways. Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A childrens park is L long and w wide. It is sorrounded by a pathway of uniform width, u.
Suppose the total area of the park and the pathway is T square meters. How wide is the pathway?

VARIABLES
system%28L=3500%2Cw=200%2CT=74464%2Cu=unknown%29

Park Area, wL
Combined Park Area and Pathway, (w+2u)(L+2u)
Combined Park Area and Pathway, T
highlight_green%28highlight%28%28w%2B2u%29%28L%2B2u%29=T%29%29----Basic Starting Equation in Symbolic Form

STEPS TOWARD SOLVING FOR u
wL%2B2Lu%2B2wu%2B4u%5E2-T=0
wL%2B%282L%2B2w%29u%2B4u%5E2-T=0
highlight_green%284u%5E2%2B%282L%2B2w%29u%2BwL-T=0%29----Quadratic equation in the unknown variable, u.

Continue as far as you can or want in purely symbolic form, and substitute the given values
when you are ready to finish. The question asks for u, the value of the uniform pathway width.


----
If you continue to find u completely symbolically, you should find the formula
highlight%28u=%28-L-w%2Bsqrt%28L%5E2-2wL%2Bw%5E2%2B4T%29%29%2F4%29
which is simplification from the general formula of a quadratic equation.