A = L × W = 450 m^2
L = W+7
So: 450m^2 = (W+7)(W)
450m^2 = W^2 + 7W
W^2 + 7W -450 = 0
Now to factor the quadratic we need to think of what factors of 450 have a difference of 7??
Well 15×30= 450, but there difference is 15. So let's try two more... 25×18= 450. Is 25-18 = 7?
YES!! So we know the factors are:
(W-18)(W+25) = 0
So W-18 = 0, W = 18m
And W+25 = 0, W = -25m
We can't have a negative length in real life, so the only true solution is W = 18m
Do the shorter side (W) is 18m long
And the longer side (L) = W + 7 = 25
So the perimeter (P) = 2 (L+W) = 2 (25+18)
P = 2 (43) = 86m
