A rectangular lawn measures 40m by 30m.?

Question

Chris cuts half the lawn by mowing strips of equal width aroung the perimeter. Jonah cuts the small rectangle left. How wide a strip does Chris have to cut so that they share the work equally?

Answer 1

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Area of lawn is 30 x 40 = 1200 square meters

If they share the work equally, each does half

1200/2 - 600 square meters

when equal strips are cut off all sides, the remaining area is

(30-2x) * (40-2x) = 600

1200-140x+4x^^2 = 600

x^^2 - 35x + 150 = 0

Use the quadratic equation to solve for the roots:

x = {-(-35) ± sqrt[ (-35)^^2-4*(1)*(150)]} / {2 *1}

x = 5 or 30

30 is more than half the width, so it does not make sense in an area problem.

To check that 5 is correct, calculate using the original equation

(30-2x) * (40-2x) = 600

(30-2*5) * (40-2*5) = 20 * 30 = 600

Chris must cut a strip 5 meters wide off each side.