SOLUTION: A 50m by 20m rectangular lawn is mowed by first cutting a uniform strip along it's perimeter. This leaves 4/5 of the lawn area uncut. Determine the width of the cut to the nearest

Question 615307: A 50m by 20m rectangular lawn is mowed by first cutting a uniform strip along it's perimeter. This leaves 4/5 of the lawn area uncut. Determine the width of the cut to the nearest hundredth of a meter.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A 50m by 20m rectangular lawn is mowed by first cutting a uniform strip along it's perimeter.
This leaves 4/5 of the lawn area uncut.
Determine the width of the cut to the nearest hundredth of a meter.
:
let w = the width of the cut
Find the area of the lawn; 50*20 = 1000 sq/m
Find 4/5 of 1000 sq/m = 800 sq/m
:
(50-2w)(20-2w) = 800
FOIL
1000 - 100w - 40w + 4w^2 = 800
A quadratic equation
4w^2 - 140w + 1000 - 800 = 0
4w^2 - 140w + 200 = 0
simplify, divide by 4
w^2 - 35w + 50 = 0
Use the quadratic formula to find w, a=1, b=-35, c=50
Only one solution will make sense: w ~ 1.49 meters

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