SOLUTION: Polynomial word problems help! A cement walk of uniform width surrounds a rectangular swimming pool that is 10 m wide and 50 m long. Find the width of the walk it its area is 86

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Question 256203: Polynomial word problems help!
A cement walk of uniform width surrounds a rectangular swimming pool that is 10 m wide and 50 m long. Find the width of the walk it its area is 864 m^2.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First draw a rectangle and label it 10m on the length and 50m on the width.
Second draw a rectangle around the pool and place an x to the left and right of the 10 and above and below the 50.
step 1 - area of pool.
A = LW = 10*50 = 500
step 2 - area of pool + walkway = 864
(i) A = %2810%2B2x%29%2850%2B2x%29+-+500+=+864
(ii) A = %284x%5E2%2B120x%2B500%29+-+500+=+864
(iii) A = 4x%5E2%2B120x+=+864
setting = 0, we get
(iv) 4x%5E2+%2B+120x+-+864+=+0
dividing by 4 and then factoring, we get
(vi) %28x-6%29%28x%2B36%29+=+0
So,
x = 6 or x = -36.
width of the walk is 6m.