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

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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) About Me  (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 aL%5E2%2BbL%2Bc=0 (in our case 2L%5E2%2B-9L%2B-100+=+0) has the following solutons:

L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-9%29%5E2-4%2A2%2A-100=881.

Discriminant d=881 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+881+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+881+%29%29%2F2%5C2+=+9.67041103982791
L%5B2%5D+=+%28-%28-9%29-sqrt%28+881+%29%29%2F2%5C2+=+-5.17041103982791

Quadratic expression 2L%5E2%2B-9L%2B-100 can be factored:
2L%5E2%2B-9L%2B-100+=+2%28L-9.67041103982791%29%2A%28L--5.17041103982791%29
Again, the answer is: 9.67041103982791, -5.17041103982791. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-9%2Ax%2B-100+%29

Answer by stanbon(75887) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!

:
Find the diagonal
d = sqrt%289.67%5E2+%2B+10.34%5E2%29
d = 14.157 is the diagonal