SOLUTION: A playground is 25m by 40m. It is surrounded by a paved skating path of uniform width. The combined area of the playground and path is 1,426 square meters. How wide is the path?

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Question 27771: A playground is 25m by 40m. It is surrounded by a paved skating path of uniform width. The combined area of the playground and path is 1,426 square meters. How wide is the path?
Found 2 solutions by Paul, Earlsdon:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
(25+x)(40+x)=1426
1000%2Bx%5E2%2B25x%2B40x=1426
x%5E2%2B65x%2B1000-1426
x%5E2%2B65x-426=0

Factor: (x+71) and (x-6)

Remove the negative left with x= 6.

Hence, the uniform path is 6cm.
Paul.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the path be x meters. You can express the combined area in terms of x:
A+=+%2825%2B2x%29%2840%2B2x%29 and this is given as 1,426 square meters, so:
%2825%2B2x%29%2840%2B2x%29+=+1426 Simplify and solve for x.
1000%2B130x%2B4x%5E2+=+1426 Subtract 1426 from both sides of the equation.
4x%5E2%2B130x-426+=+0 Solve this quadratic equation by factoring. First, factor out a 2.
2%282x%5E2%2B65x-213%29+=+0 Apply the zero products principle.
2x%5E2%2B65x-213+=+0 Factor this.
%282x%2B71%29%28x-3%29+=+0 Apply the zero products principle.
%282x%2B71%29+=+0 and/or %28x-3%29+=+0
If2x%2B71+=+0 then 2x+=+-71 and x+=+-35.5 Discard this solution as the path width must be a positive number.
If x-3+=+0, then x+=+3
The width of the path is 3 meters