SOLUTION: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width. if the area of the pool and the path combined is 600 square meters, what is the width of the path?

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Question 202338: A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width. if the area of the pool and the path combined is 600 square meters, what is the width of the path?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the path width = x meters.
The area of the pool and path combined can be expressed by:
A+=+%2810%2B2x%29%2820%2B2x%29
A+=+200%2B60x%2B4x%5E2 and this is equal to 600 sq.meters., so we substitute A+=+600 and rearrange the equation a bit.
4x%5E2%2B60x%2B200+=+600 Now subtract 600 from both sides to get it into standard form for a quadratic equation.
4x%5E2%2B60x-400+=+0 Factor out a 4 to ease the calculations a bit.
4%28x%5E2%2B15x-100%29+=+0 So we now have:
x%5E2%2B15x-100+=+0 Factor this quadratic equation.
%28x-5%29%28x%2B20%29+=+0 Applying the zero product rule, we get:
x+=+5 or x+=+-20 Discard the negative solution as the path width, x, must be a positive value.
The width of the path is 5 meters.
Check:
600+=+%2810%2B2x%29%2820%2B2x%29 Substitute x = 5 meters.
600+=+%2810%2B10%29%2820%2B10%29
60+=+%2820%29%2830%29
600+=+600 OK!