11. For a math homework assignment, Karla found the

area and perimeter of a room of her house. She

reported that the area of her rectangular living room is

180 square feet and that the perimeter is 54 feet. When

drawing a sketch of her living room the next day, she

realized that she had forgotten to write down the

dimensions of the room. What are the dimensions of

Karla's living room, in feet?

A. 9 by 20

B. 10 by 18

C. i2 by 15

D. 14 by 13

E. 16 by 11

Option C. 12 by 15

Step-by-step explanation:

Let the length be L

Let the width be w

Area of rectangle = L x w

Perimeter of rectangular = 2 (L + w)

From the question given,

A = 180

P = 54

180 = L x w (1)

54 = 2 (L + w) (2)

From equation (2),

54 = 2 (L + w)

Divide both side by the 2

54/2 = L + w

27 = L + w

L = 27 - w (3)

Substituting the value of L into equation (1), we have:

180 = L x w

180 = w (27 - w)

180 = 27w - w^2

Rearrange the expression

w^2 - 27w + 180 = 0 (4)

Solving by factorization method:

Multiply the first term (i. e w^2) with the last term (i. e 180). This gives 180w^2. Now find two factors of 180w^2, such that their sum will result to the second (i. e - 27w). These factors are - 12w and - 15w.

Now, substitute these factors (-12w and - 15w) into equation (4)

w^2 - 27w + 180 = 0

w^2 - 12w - 15w + 180 = 0

w (w - 12) - 15 (w - 12) = 0

(w - 12) (w - 15) = 0

w = 12 or w = 15.

Substituting the value of w into equation (3)

L = 27 - w

When w = 12

L = 27 - 12 = 15

When w = 15

L = 27 - 15 = 12

Since the length is longer than the width, the length is 15 and the width is 12.

Therefore the dimensions is 12 x 15