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

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Answer:

12 feet and 15 feet

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

User Ahmad Dalao
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