What is the length of the diagonal of the square shown below?

Question

anonymous · Answer

attachment

whpalmer4 · Answer

You've got a right triangle, with the two non-hypotenuse sides being 7 in length.
$$a^2+b^2= c^2$$
$$7^2+7^2=c^2$$
What is the value of c?  That's the diagonal.

anonymous · Answer

98

whpalmer4 · Answer

Let's think about this a little more.  You've got a triangle with two legs that are both 7, and the 3rd leg is going to be 98?!?

whpalmer4 · Answer

Agree that something isn't quite right there?

anonymous · Answer

yes so its $$10 \sqrt{7}$$

whpalmer4 · Answer

Well, closer...but still wrong.  What is $10\sqrt{7}*10\sqrt{7}$?  If the square root of 7 is bigger than 1, that's going to be bigger than 98, isn't it?  After all, $10*10 = 100$

whpalmer4 · Answer

We need to take the square root of $c^2=98$ to find our answer.  If we take the square root of the left side, that's $c$, no problem there.  But what is the square root of 98?

Can you write a factorization of 98 with prime numbers?  (2, 3, 5, 7, 11, 13, etc.)?

whpalmer4 · Answer

$$sqrt{98} = \sqrt{2*7*7} = 7\sqrt{2} \approx 9.899$$