Answer 1

We have,

ABCD is a rhombus with side 10 cm and diagonal BD = 16 cm

We know that diagonals of a rhombus bisect each other at 90°

∴ BO = OD = 8 cm

In ΔAOB, by pythagoras theorem

AO² + BO² = AB²

⇒ AO² + 8² = 10²

⇒ AO² = 100 − 64 = 36

⇒ AO = `sqrt36` = 6 cm          [By above property]

Hence, AC = 6 + 6 = 12 cm