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:
 |
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
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Cheers,
Stan H.
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