A rectangle Has an area of 105 ft.² if the sum of the length and width is 26 feet find the dimensions include units

llm

Answered on Sun Apr 10 2022

Let length of rectangle be x and width of rectangle be y

Area of rectangle = 105 ft^2

Length x width = 105ft^2

x * y = 105 …..1

Sum of length and width = 26 feet

Length + width = 26 feet

x + y = 26 ……2

from equation 2

y = 26 - x

now, putting value of y in equation 1, we get

x * 26 -x = 105

26x - x^2 = 105

x^2 - 26x + 105 = 0

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

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

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

So, x = 5 and x = 21

So, when length = 5 ft

width, y = 26 - 5 = 21 ft

And, when length = 21 ft

Then, width , y = 26 - 21 = 5 ft

So, the possible dimensions of rectangle are (5,21) and (21,5).