This is the representation: l (length) , w (width)
lw = 200
2l + 2w = 60 --------- l = 30 - w
I'll use the substitution method. Since l = 30 - w, we can substitute the length to 30 - w to lw = 200.
(30 - w) w = 200
-w² + 30w = 200 ------------- transpose -w² + 30w
w² - 30w + 200 = 0 --------------- use factoring
(w - 20) (w - 10) = 0 -------------- then equate each factor to zero
w - 20 = 0 w - 10 = 0
w = 20 w = 10
then substitute the value of w to any of the equations to get the value of l.
lw = 200 lw = 200
l (20) = 200 l (10) = 200
l (20)/20 = 200/20 l (10)/10 = 200/10
l = 10 l = 20
So the answers to the problem are:
width = 20 then length = 10 or
width = 10 then length = 20
