Question

PQRS is a parallelogram
with PQ = 15 cm, ST
= 10 cm, and QV = 12 cm.
Find PS.
10 cm
12 cm find ps
​

Answer 1

Answer:

Given: PQRS is a parallelogram. PQ=15 and RQ=10, LPRL=32

In △RLQ and △NLP

∠RLQ=∠NLP (vertically opposite angles)

∠LRQ=∠LPN (Alternate angles)

∠LQR=∠LNP (Alternate angles)

Thus, △RLQ∼△PLN (AAA rule)

Hence, PLRL=PNRQ (Corresponding sides of similar triangles)

PN=23×10

PN=15cm

Similarly, △RLM∼△PLQ

LPRL=PQRM (Corresponding sides of similar triangles)

RM=315×2

RM=10 cm.