SOLUTION: The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 122 square centimeters, what is the length of the diagonal?

Algebra.Com
Question 946706: The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 122 square centimeters, what is the length of the diagonal?
Answer by amarjeeth123(574)   (Show Source): You can put this solution on YOUR website!
Let the length of the rectangle be x.
Width of the rectangle=2x-5
Area of the rectangle=x(2x-5)
x(2x-5)=122
2x^2-5x-122=0
x^2-2.5x-61=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=250.25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 9.15964600977819, -6.65964600977819. Here's your graph:

x=9.16
2x-5=13.32
Length of the diagonal=16.16
RELATED QUESTIONS

the length of a rectangle is 5 centimeters less than twice its width. the perimeter if... (answered by solver91311)
The length of a rectangle is 3 centimeters less than its width. What are the dimensions... (answered by ramkikk66)
The length of a rectangle is 3 centimeters less than its width. What are the dimensions... (answered by Alan3354)
the length of a rectangle is 12 centimeters less than its width what are the dimensions... (answered by tenkun)
the length of a rectangle is 6 centimeters less than its width. what are the dimensions... (answered by macston)
The length of a rectangle is 4 centimeters less than its width. What are the dimensions... (answered by Cromlix)
The length of a rectangle is 6 centimeters less than its width. What are the dimensions (answered by ikleyn)
The length of a rectangle is 3 centimeters less than its width. What are the dimensions... (answered by josgarithmetic)
the length of a rectangle is 2 centimeters less than its width. What are the dimensions... (answered by Alan3354)