Question

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

Answer 1

Answer:

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