Question

A rectangle has an area of 105 square feet. If the sum of the length and width is 26 feet, find the dimensions.

Answer 1

x+y=26, y=26-x

a=xy, using y from above:

a=x(26-x)

a=26x-x^2, and we are told that a=105

105=26x-x^2

x^2-26x+105=0

x^2-5x-21x+105=0

x(x-5)-21(x-5)=0

(x-21)(x-5)=0

So the dimensions are 5 ft by 21 ft.