SOLUTION: The length of a rectangular picture is 5 cm more than the width. The area is 84 cm^2. Find the length and width

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Question 357105: The length of a rectangular picture is 5 cm more than the width. The area is 84 cm^2. Find the length and width
Answer by neatmath(302)   (Show Source): You can put this solution on YOUR website!
Let l be the length. Let w be the width.

Thus, we know:

and

We can use this information to solve:







We then need to factor this equation, or use the quadratic formula, like this:

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=361 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7, -12. Here's your graph:


Since the width has to be a positive number, we know that the width is 7, and we can discard the -12 solution.

Then, we have:







Then, our answer is: the length is 12 cm, and the width is 7 cm.

I hope this helps!
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