One of the sides of the rectangle is 8cm what is the adjacent side if it is 3 times smaller than the diagonal.

Let the unknown side of the rectangle be a, then the diagonal is 3 * a.

The adjacent sides and the diagonal of the rectangle form a right-angled triangle, for which, according to the Pythagorean theorem:

8 ^ 2 + a ^ 2 = (3 * a) ^ 2;

64 + a ^ 2 = 9 * a ^ 2;

8 * a ^ 2 = 64;

a ^ 2 = 64/8 = 8;

a = √8 = 2√2 cm – the desired side of the rectangle.