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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