Question

ABCD is a square of side a unit. find the length of diogonal Ac.

Answer 1

Let the side length s of square ABCD,
the length of the diagonal Ac is s√2

This is due to Pythagoras’s theorem. For all right triangles with legs of length a and b and with hypotenuse of length c,
it holds true that a^2+b^2=c^2.

This equation can be rearranged to solve for the length of the hypotenuse: c=√a^2+b^2

The diagonal of a square is essentially the hypotenuse of a right triangle whose legs are of the same length.
All sides of squares are congruent, so the equation becomes c=√2a^2

Finally, we can pull out the a^2 from under the radical symbol to obtain c=a√2.