Question

Given an isosceles triangle with vertex angle 90°. You drop a line segment from the vertex to the opposite side, to intersect at the midpoint. The segment you drew has a length of 3cm. Why & how is the length of one of the isosceles sides 3 square root of 2 and not 3?

Answer 1

Basically, you are bisecting the vertex angle AND the base of a 90 45 45 triangle, which creates two side by side 90 45 45 triangles.
The legs of the original triangle = 3^2 + 3^2.
leg^2 = 18
leg = 3 * sqroot (2)