A room has an area of 456 square feet. One dimension is 5 feet more than the other. Find the dimensions of the room.

L * W = A.

L + 5 = W

Substitute (L + 5) for W in the first equation.

L (L + 5) = A = 456.

distribute the L.

L² + 5L = 456

L² + 5L - 456 = 0

(L + 24) (L - 19) = 0

L = - 24 and L = 19.

Because 19 is positive L = 19.

Because 24 is 5 more than L and when multiplied by L = 456, W = 24.