Please Answer this Question.   Joanne has a garden that is 9 feet long by 6 feet wide. She wants to increase the dimensions of the garden by the same distance each way and have the area of the new garden be five times the area of the present garden. How many feet should she add to both the width and the length?  

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What you are going to end up doing here is setting up and solving a quadratic equation.

You know that you have to increase both dimensions by the same number -- we'll call that x.

So you are going to have

(x+9)(x+5) = 270

This is because you have to...

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What you are going to end up doing here is setting up and solving a quadratic equation.

You know that you have to increase both dimensions by the same number -- we'll call that x.

So you are going to have

(x+9)(x+5) = 270

This is because you have to multiply the new dimensions to get the new area.  And the new area is 54*5=270.

When you multiply out the left side, you end up with

x^2+15x+54=270

And that can become

x^2+15x-216 = 0

So then you just have to factor and that would get you

(x+24)(x-9) = 0

Which means that

x = -24 or x = 9

Of course, you're not going to subtract 24 feet from each side, so the answer is that you need to add 9 feet to each side.

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