The length of a rectangle is 5 ft less than twice the width, and the area of the rectangle is 33 ft2 . find the dimensions of the rectangle. explanation

Hi there!

For this question, we can set up a systems of equations.
Let's say that length : x , width : y.

x = 2y - 5
xy = 33
use substitution
(2y - 5)y = 33

2y² - 5y = 33
subtract 33 on both sides to make the equation equal to zero.

2y² - 5y - 33 = 0
factor it

(2y - 11)(y + 3) = 0
2y - 11 = 0               y + 3 = 0
2y = 11
y = 5.5                         y = -3 (ignore this -3. You can't have a negative width)

substitute 5.5 in xy = 33
5.5x = 33
x = 6

Check it you are right...
6 = 2(5.5) - 5
6 = 11 - 5
6 = 6

So your final answers are
Length : 6 ft
Width : 5.5 ft

Hope this helped!! :)