Quadrangle ABCD is a rhombus with side AB = 17cm, diagonal BD = 30cm. Find the length of the AC diagonal.

The diagonals of the rhombus intersect at point O, form four equal right-angled triangles. Consider one of them, triangle AOB, in it:
AB = 17 cm (by condition);
ОВ = 1/2 * ВД = 15 cm (property of rhombus diagonals).
By the Pythagorean theorem, we find the leg OA:
ОА = √ (AB² – OB²) = √ (17² – 15²) = √ (289 – 225) = √64 = 8 (cm).
Find the AC diagonal:
AC = 2 * OA = 16 (cm).
Answer: the length of the AC diagonal is 16 cm.