The area of a living room is 180 square feet and the perimeter is 54 feet. What are the dimensions in feet?

12 feet and 15 feet

Step-by-step explanation:

perimeter = p

perimeter of a rectangle = 2*L + 2*w

area of a rectangle = L*w

w = width

L = length

the statement tell us:

area = 180 square feet = area of a rectangle

p = 54 feet

so we have:

180 = L*w equation 1

54 = 2*L + 2*w equation 2

using equation 2 we have:

2L = 54 - 2w

L = (54-2w) / 2

L = 27 - w equation 3

using equation 3 in equation 1 we have:

180 = (27 - w) * w

180 = 27w - w^2

w^2 - 27w + 180=0

using quadratic equation : ax^2 + bx + c = 0

with a = 1 b = - 27 c = 180

we have:

w = 12 feet = width

L = 27 - 12 = 15 feet = length

the dimensions are 12 feet and 15 feet