Question

If the sides of a square measure 9√3 units, then find the length of the diagonal.

Answer 1

22.045

a^2+b^2=c^2

So you square the length of the side of the square, you then get 486 and take the square root and you get 22.045

Answer 2

9514 1404 393

Answer:

9√6 units

Explanation:

You know that the diagonal of a square is √2 times the length of one side, so the diagonal of your square is ...

diagonal = (√2)·side

diagonal = √2·9√3 = 9√(2·3)

diagonal = 9√6

_____

In case you hadn't committed that relationship to memory, you could figure it out from the Pythagorean theorem:

d² = s² + s²

d² = 2s² . . . combine terms

d = s√2 . . . take the square root