Question

(i) In the figure given below, OPQRS is a trapezium SR PQ. S = 45°, R = 30°
PQ = 4, QR = 12, then find the length of SR.
P
4
O
2
45
30
S
A
B
R​

Answer 1

Answer:

In △QRS, SR=4 cm and ∠SQR=45

o

and ∠QRS=90

o

Then in △QRS, we have

tan45

0

=

PQ

SR

⇒1=

PQ

4

⇒PQ=4 cm

In trapezium PQ∣∣VR, then PQ=PT=4 cm

In △PTV, ∠TPV=60

o

and PT=4 cm

⇒tan60

0

=

PT

VT

⇒

3

=

4

VT

⇒VT=4

3

cm

But VR=VT+TS+SR, where PQ=TS=6 cm ....given

⇒VR=4

3

+6+4=10+4

3

cm