polynomial inequalities?

Question

the perimeter of a rectangle is 50feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 114 sq feet.

Looking for a solution set. The sides in feet are [?,?] or [?,?]

Answer 1

Hello,

2l + 2w = 50 so l = 25 - w

lw <= 114 put in l = 25 -w and we have (25-w)(w) <= 114 so

25w -w^2 >= 114 or w^2 -25w + 114 <=0 Factor (x-6)(x-19) <= 0 then (x-6) <=0 and (x-19)>=0 or (x-6)>=0 and (x-19)<=0 so
x<=6 and x>=19 Empty or x>+6 and x<=19 the 6,+x<=19.Feet

[6,19]

Hope This Helps!