SOLUTION: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How

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Question 49005: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be? Please solve and explain.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Assuming that the sidewalk will be of uniform width around the lawn, let's call the width of the sidewalk x feet.
With the dimensions given in the problem, the dimensions of the remaining lawn after the sidewalk is constructed will be:
(32-2x) by (24-2x) and its area is given as 425 sq.ft.
So you can write the equation for the area of the new lawn as:
Simplify this and solve it for x, the width of the sidewalk.
Subtract 425 from both sides of the equation.
Solve this quadratic for x by factoring.
Apply the zero product principle.
and/or
If then and
If then and
As you would expect, we have two solutions to this quadratic equation...but only one of them is meaningful in terms of the width of the sidewalk. Let's look at them one-at-a-time.
= 24.5 feet This is not meaningful because the original lawn is only 24 feet wide and if you built a sidewalk this wide, you would have no lawn left. So, discard this solution.
= 3.5 feet. This solution works. Let's check!
Substituting x = 3.5
Simplify.

It checks!