Question

If the lenght of each side of rhombus pqrs is 8 cm and its ant pqr is 120 degree find the side qs

Answer 1

Answer: 8 cm

Step-by-step explanation:

The properties of rhombus which we will use in this question:

(i) The diagonals of a rhombus bisects the vertex angle

(ii) The diagonals of a rhombus bisect each other at right angles

_____

Refer the attachment for the figure.

Construction: Join QS and PR

According to property (i):

/_SQR = /_QSR = $\tt{\frac{1}{2}}$/_PQR = 60°

According to property (ii):

/_O = 90°

In triangle OQR:

By using:

cos 60 = $\tt{\frac{1}{2}}$

We get:

$\tt{\frac{OQ}{QR} = \frac{1}{2}}$

OQ = 4 cm

According to property (ii):

OQ = OS = 4 cm

QS = OQ + OS = 4 + 4

QS = 8 cm