Question 934227: Lisa, Nicole, and Amber are to mow a rectangular lawn that measures 100 feet by 120 feet. Lisa is going to mow one-third of the lawn by mowing a strip of uniform width around the outer edge of the lawn. What are the dimensions of the lawn to still be mowed?
Thx for you help! :D
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Lisa, Nicole, and Amber are to mow a rectangular lawn that measures 100 feet by 120 feet.
Lisa is going to mow one-third of the lawn by mowing a strip of uniform width around the outer edge of the lawn.
What are the dimensions of the lawn to still be mowed?
:
Find the area of the lawn; 100 * 120 = 12000 sq/ft
Find 2/3 (the unmown area) 2/3 * 12000 = 8000 sq/ft
:
Let x = the width of the strip to be mowed by Lisa
:
(100-2x)(120-2x) = 8000
FOIL
12000 - 200x - 240x + 4x^2 = 8000
Arrange as a quadratic equation
4x^2 - 440x + 12000 - 8000 = 0
4x^2 - 440x + 4000 = 0
simplify, divide by 4
x^2 - 110x + 1000 = 0
factors to
(x-100)(x-10) = 0
Two solutions
x = 100, not a likely solution
and
x = 10 ft is the width of strip mowed by liza
:
"What are the dimensions of the lawn to still be mowed? "
x = 10 means the original dimensions will be reduced by 20 ft
80 by 100 is the dimensions of the unmowed portion
:
:
Confirm this by finding the area: 80*100 = 8000 which is 2/3 of the original area
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