SOLUTION: A rectangle building measures 20m by 15m . It is surrounded by a path of uniform width. If the area of the uniform width is 156 m^2 , find its width .
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Question 1152072: A rectangle building measures 20m by 15m . It is surrounded by a path of uniform width. If the area of the uniform width is 156 m^2 , find its width . Found 2 solutions by MathLover1, ikleyn:Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website! A rectangle building measures
It is surrounded by a path of uniform width .
If the area of the uniform width is , find its width .
to the both, length and width of the building, add (one on each side)
the area of the uniform width is:
.......use quadratic formula to calculate .......simplify
..........we need only positive solution for width
so,
-> exact solution
The answer by @MathLower1 is absurdist and incorrect.
The answer CAN NOT be negative in such problems.
The reason why her answer is absurdist, is in that the problem' setup is incorrect, and, hence, the entire solution is wrong.
Below find my correct solution.
The dimensions of the larger rectangular area are 20+2w meters by 15+2w meters,
so the area of the larger rectangle is (20+2w)*(15+2w) square meters.
The area of the building itself is 20*15 = 300 square meters.
We are given that
(20+2w)*(15+2w) - 300 = 156 square meters.
To find w from this equation, simplify it step by step
300 + 4w^2 + 70w - 300 = 156
4w^2 + 70w - 156 = 0
= = .
Of the two roots, only positive w = = 2 is the solution to the problem.
ANSWER. The path width is 2 meters.
CHECK. (20+2*2)*(15+2*2) - 300 = 156 square meters. ! Precisely correct !
