SOLUTION: The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 100 centimeters squared, what is the length of the diagonal? So far i have this: W= 2L

Question 213061: The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 100 centimeters squared, what is the length of the diagonal?
So far i have this:
W= 2L-9
L= ?
L(2L-9)=100
2L^2-9L-100=0
I tried to factor it and used the quadratic formula and I still couldn't get answer.
Please help. Thank you!
Found 3 solutions by nerdybill, stanbon, ankor@dixie-net.com:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 100 centimeters squared, what is the length of the diagonal?
So far i have this:
W= 2L-9
L= ?
L(2L-9)=100
2L^2-9L-100=0
.
Let L = length
then
2L-9 = width
.
L(2L-9) = 100
2L^2-9L = 100
2L^2-9L-100 = 0
.
You can solve it using the quadratic equation. Doing so yields:
L = {9.67, -5.17}
We can throw out the negative solution leaving:
L = 9.67 centimeters
.
Width then is:
2L-9 = 2(9.67)-9 = 19.34-9 = 10.34 centimeters
.
To find the diagonal, you apply Pythagorean theorem:
19.34^2 + 9.67^2 = d^2
467.5445 = d^2
21.62 centimeters = d (diagonal)
.
Details of quadratic to follow:

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=881 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.67041103982791, -5.17041103982791. Here's your graph:

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 100 centimeters squared, what is the length of the diagonal?
So far i have this:
width = W= 2L-9
length = L
L(2L-9)=100
2L^2-9L-100=0
L = [9 +- sqrt(81 - 4*2*-100)]/4
---
L = [9 +- sqrt(881)]/4
Positive solution:
L = [9 + 29.68]/4
Length = 9.67 cm
Width = 2(9.67)-9 = 10.34
==============================
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!

:
Find the diagonal
d =
d = 14.157 is the diagonal

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