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The diagonal can be found by taking length^2+width^2=diagonal^2

13^2=x^2+(x+7)^2

169 = x2 + x2 + 14x + 49

120 = 2x2 + 14x

x2 + 7x - 60 = 0

now just factor, and you have the answer. It's the positive x value.

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