Question 1089290
L x W = Area
L x (L-2) = 48
L^2-2L = 48
The coefficient of L is -2. Divide it by 2 and you get -1. Square -1 and add to both sides to make the perfect square:
L^2-2L+(-1)^2 = 48+(-1)^2 = L^2-2L+1 = 49
(L-1)^2 = 49
sqrt(L-1)^2 = sqrt49
L-1 = 7 or L-1 = -7
L = 8 or L = -6
We are not looking for a negative, so let's try the 8:
L x (L-2) = 48
8 x (8-2) = 48 Correct.