Question: Susie is designing a stand for an exhibition. It is to have display screens round three sides and to be open on the other side. 40 m of screens are available for the stand and the owners want a rectangular floor space of at least 150 square metres.

What limits must Susie work within for the lengths of the sides of the stand?

total length of screen = 40 + 40 + 40 = 120

perimeter = 2l + w

2l +w = 120

w = 120 -2l

or $\displaystyle l =60 - \frac{1}{2}w $

$\displaystyle w(60 - \frac{1}{2}w)\geq 150 $

$\displaystyle 60w-\frac{1}{2}w^2\geq 150$

i need up with this but $\displaystyle w^2-120w+300\leq 0 $

can some one tell me what i am doing wrong

thank you for helping me