Problema Solution
two landscapers must mow a rectangular lawn that measures 100 feet by 200 feet. each wants to mow no more than half of the lawn. the first starts by mowing 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? work
Answer provided by our tutors
let 'x' represent the width of the strip, x>0
100*200 - (100 - 2x)(200 - 2x) <= (1/2)(100*200)
-x^2 + 150x - 2500 <=0
by solving
-x^2 + 150x - 2500 = 0
we find
x1 = 131 ft this is not a solution because x <= 100
x2 = 90 ft
by drawing the graph y = -x^2 + 150x - 2500 we see the solutions are [0, 90]
click here to see the graph: