SOLUTION: The length of a rectangle is 6 cm more than the width. The area is 11 cm^2. Find the length and width.

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Question 991021: The length of a rectangle is 6 cm more than the width. The area is 11 cm^2. Find the length and width.
Answer by Timnewman(323)   (Show Source): You can put this solution on YOUR website!
Hi dear,
let L=lenght,
w=width
Then,from your question,
L=w+6-----(1)
and
L*w=11----(2)
Put 1 in 2,
(w+6)w=11
w²+6w-11=0
Solve the resulting quadratic equation as follows:
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=80 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.47213595499958, -7.47213595499958. Here's your graph:

Then w=1.5cm,w=-7.3cm
When w=1.9,
L=1.9+6
L=7.9cm
when w=-7.3,
L=-7.3+6
L=-1.3cm
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