Expert: Ahmed Salami - 8/13/2009

Question
Express the length d of a squares diagonal as a funtion of its side length

Answer
Hi Caitlin,
The triangle containing the diagonal of a square and two of its sides is a right-angle triangle, which means that the Pythagoras' Theorem applies to it.
The theorem states that if a and b are the two sides of a right triangle and c is the diagonal, then
c² = a² + b²
Now, if the square has sides of length l and diagonal d
d² = l² + l²
d² = 2l²
Taking square roots of both sides,
√d² = √2.√l²
d = l√2

Regards