SOLUTION: The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 33 cm^2, what is the length of the diagonal?

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Question 211150: The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 33 cm^2, what is the length of the diagonal?
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
L=w+1
wL=A
w(w+1)=33
w^2+w-33=0
w=5.266... Quadratic formula
L=6.266...
.
a^2+b^2=c^2
(5.266)^2+(6.266)^2=67
sqrt(67)cm is the length of the diagonal.
.
Ed
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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=133 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5.2662812973354, -6.2662812973354. Here's your graph:
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