A room has an area of 60 square meters and a perimeter of 32 meters. What are the length and width of the room

P = 32 A = 60

P = 2 (W + L) = 32 A = W x L = 60

W + L = 32 / 2

W + L = 16

We need solve one of the variables

W + L = 32 W x L = 60

(W + L) - L = 16 - L W = 60 / L

W = 16 - L

We have 2 different expressions that both equal W

16 - L = 60 / L

16 - L - (16 - L) = 60 / L - (16 - L)

60 / L - (16 - L) = 0

Multiply both sides by L to get rid of fraction

L (60 / L - 16 + L) = 0L W = 60 / L

60 - 16L + L ^ 2 = 0 W = 60 / 8 = 7.5

L ^ 2 - 16L + 60 = 0 W = 7.5

L = (L - 8) x (L - 8)

L = 8