Given: ABCD is a rectangle. The area of the rectangle is 132 square feet and the perimeter of the rectangle is 46 feet. AB > BC. Find the length of AB and BC.

Solution:

since ABCD is a rectangle, so AB = DC = x and AD = BC = y

area of the rectangle is 132 square feet

x y = 132 ... equation1

perimeter of the rectangle is 46 feet

2(x + y) = 46 ...equation2

from equation2, (x + y) = 46/2 = 23

express x in terms of y

x = 23 - y

substitute the expression of x into equation1

(23 - y) y = 132

remove parenthesis

23y - y^{2} = 132

move the number to the left side of the equation since the degree of the variable is 2

23y - y^{2} - 132 = 0

multiply (-1) in each term of the equation and write them in degree decrease order

y^{2} - 23y + 132 = 0

left side of the equation is a two degree polynomial, factoring it