Question

Diagonals of UK and HS of a rhombus HUSK are of the length 10cm and 24cm. Find its sides.

Answer 1

Step-by-step explanation:

In rhombus HUSK,

UK = 10 cm

HS = 24 cm

As diagonals of a rhombus bisect each other

So, OK = 1/2 of UK

= (1/2×10) cm

= 5 cm

So, OS = 1/2 of HS

= (1/2×24) cm

= 12 cm

Triangle OKS is a right angled triangle (Property of rhombus)

By P. Theorem

OS^2 + OK^2 = KS^2

(12 cm)^2 + (5 cm)^2 = KS^2

144 cm^2 + 25 cm^2 = KS^2

169 cm^2 = KS^2

KS^2 = 169 cm^2

KS = 13 cm

All sides of a rhombus are equal in length (Property of rhombus)

So each side of the rhombus measures 13 cm