SOLUTION: A rectangular lawn, 100 feet long by 50 feet wide, is to have two sidewalks installed that will cut the lawn in half both ways, the short way and the long way, meeting in the middl

Question 1159224: A rectangular lawn, 100 feet long by 50 feet wide, is to have two sidewalks installed that will cut the lawn in half both ways, the short way and the long way, meeting in the middle so that the lawn is divided into four equal sections. The sidewalk must occupy an area no more than 10% of the total lawn area. How wide can the sidewalk be?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Let the width of the walk be x.

Then the area of the walk is the area of a 100-foot long strip, plus the area of a 50-foot long strip, minus the area of the overlap of those two strips.

We want to find the widest the walk can be so that it is no more than 10% of the total area. So we need to find the width for which the area of the walk is equal to 1/10 of the total area of 50*100=5000 square feet.

That quadratic doesn't factor, so use the quadratic formula or some other tool to find the answer.

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