Lisa, Nicole, and Amber are to mow a rectangular lawn that measures 100 feet by 120 feet. Lisa is going to mow one0third of the lawn by mowing a strip of niform width around the outer edge of the lawn. What are the dimensions of the lawn to still be mowed?

Answer 1

total area = 12000 ft^2
still to be mowed = (1/2)(12000) = 8000 ft^2

let the width mowed by Lisa be x ft wide
area still to be done
= (100-2x)(120-2x)
= 12000-200x - 240x + 4x^2

4x^2 - 440x + 12000 = 8000
x^2 - 110x + 1000 = 0
(x-100)(x -10) = 0
x = 100 or x = 10 , but clearly
100-2x > 0
-2x > -100
x < 50

so x = 10 and the lawn left to be cut is
80 by 100 ft