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?

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) (Show Source):
You can put this solution on YOUR website!
(25+x)(40+x)=1426

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

Remove the negative left with x= 6.

Hence, the uniform path is 6cm.
Paul.

Answer by Earlsdon(6103) (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:
and this is given as 1,426 square meters, so:
Simplify and solve for x.
Subtract 1426 from both sides of the equation.
Solve this quadratic equation by factoring. First, factor out a 2.
Apply the zero products principle.
Factor this.
Apply the zero products principle.
and/or
If then and Discard this solution as the path width must be a positive number.
If , then
The width of the path is 3 meters