Do not know how to even begin/

Question

two lanscapers must mow a rectangular lawn that measures 100 ft by 200ft. Each wants to mow no more than half of the lawn. The first starts by moving around the outside of the lawn. How wide a strip must the first landscaper mow on each of the four sides in order to mow no more than half of the lawn?

Answer 1

The inside rectangle of lawn to be mowed by the other mower will have dimensions

 

(100-2w)(200-2w)=(100)200/2

 

where w is the width of the perimeter mowed by the outer mower. 

 

Useing F.O.I.L to expand the above equation

 

20000-600w+4w**2=10000

4w**2-600w+10000=0

 

using the quadratic formula to solve for w

 

w=[600+-sqrt(360000-4(4)10000)]/8

 

w=75+-25sqrt(5)

 

w=75+-56

 

w=19 ft

 

Discard the positive solution the w we are looking for must be less than 1/2 either dimension (100 or 200)

 

Check by putting w into the original equation 

(100-38)(200-38)=10000

 

which is half the total area of the 100ftx200ft lawn.