The lengths of the diagonals of a rhombus are 16 cm and 30 cm, respectively. What is the perimeter of the rhombus?

68

AO can be written as (\(\frac{AD}{2}\))= \(\frac{16}{2}\)= 8 cm

And, DO can be written as (\(\frac{BD}{2}\))

= \(\frac{30}{2}\) = 15 cm

Then, consider the triangle AOD and apply Pythagoras theorem, 

AD² = AO² + DO²

AD² = 8² + 15²

AD² = 64 + 225 = 289

AD = 17 cm

The perimeter of rhombus = 4 × side of the rhombus

= 4 × 17 = 68 cm