0
$\begingroup$

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?

Thank you for your help!

  • 0
    Whoa! I did not notice that at all! thank you guys! I have to practice more haha2012-02-27

1 Answers 1

2

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.

(I don't understand why you are working with "half diagonals" and all the rest...)

  • 0
    Oh man thanks a lot! It's a good thing I posted it here because I would have never noticed that it was so easy in the first place! Thank you so much!2012-02-27