# Question about the diagonal of a square

The question states "Find the side of a square whose diagonal is 5 feet longer that its side". It seems easy but I'm not sure about my answer. Since I know that a square has equal sides, I assign $x$ and the diagonal is $x+5$. That means that half of a diagonal is $\sqrt{x^2-(\frac{x+5}{2})^2}$. So I thought that a whole diagonal would equal two of these so $x+5 = 2\sqrt{x^2 - (\frac{x+5}{2})^2}$ and I got $5+5\sqrt{2} ft$. Is this right?

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Why are you working with half diagonals? – Arturo Magidin Feb 27 '12 at 6:23
What should I be doing? I thought I could use half diagonals to use the Pythagorean theorem. – Juan de la John Feb 27 '12 at 6:24
Hint: By the Pythagorean Theorem, $x^2+x^2=(x+5)^2$. – André Nicolas Feb 27 '12 at 6:25
You can use the Pythagorean Theorem directly with the entire diagonal. Your answer is correct, but it looks to me that you did way too much work to get it. – Arturo Magidin Feb 27 '12 at 6:26
Whoa! I did not notice that at all! thank you guys! I have to practice more haha – Juan de la John Feb 27 '12 at 6:31

If the side of the square is $x\gt 0$, then the length of the diagonal is $\sqrt{x^2+x^2} = x\sqrt{2}$ (the diagonal, the base, and the corresponding side give you a right triangle with the diagonal as hypothenuse). So you are assuming that $x+5 = x\sqrt{2}$. From here, you can solve for $x$ rather easily.