If the side length of a square is 5, what is length of the diagonal?

Question

round answer to the nearest tenth.

Answer 1

Since a square with side length of 5 would have all sides equal to 5, then the diagonal would be the square root of 5.  That's because by the Pythagorean theorem, a^2 + b^2 = c^2, where c is the diagonal which cuts through the middle of the square.  In any square, the diagonal will be equal to side length times square root of 2.  So for your problem, the answer is 5 times the square root of 2.  

 

5^2 + 5^2 = c^2

25 +25 = c^2

50 = c^2, so c = square root of 50, which is 7.071067812 (by calculator), or 5 x square root of 2, which is:

5 x 1.414213562 = 7.071067812

 

Here's the deal:  If you know the side of a square, then the diagonal will ALWAYS be the side length x square root 2...

But, we never need to express the diagonal in decimal form (unless that's what's requested).  Instead, we just say side length of the square times the square root of 2.