Solve this: Q14 In the given figure, 3SR = 2SP ,ST || PM and ar ( ∆PMR) = - Maths - Triangles

Question

Solve this:

Q14 In the given figure, 3SR = 2SP ,ST || PM and ar ( ∆ PMR)
= 50 cm2 Calculate

(a) ar ( ∆ RST ) (b) ar ( □ PMTS)

Shruti Tyagi · Accepted Answer

Dear student,

In ∆RPM and ∆RST∠R=∠R --[common]∠RPM=∠RST   --[alt angles as ST∥PM]⇒∆RPM~∆RST   --[by AA criterion]⇒RPSR=RMRT=PMSTNow, area ∆RSTarea ∆RPM=SRRP2   --(1)   --[Ratio ofsimilar triangles is equal to the square of corresponding sides]=SRSR+SP2   given 3SR=2SP⇒SRSP=23    ⇒PR= SR+SP⇒PR=2+3⇒PR=5⇒area ∆RSTarea ∆RPM=252     --[using (1)]=425⇒area ∆RSTarea ∆PMR=425(a) Thus, area ∆RST=4 cm(b) area trapezium PMTS=area ∆PMR-area ∆RST⇒ area trapezium PMTS=25-4=21 cm 
Regards

Solve this: Q14. In the given figure, 3SR = 2SP ,ST || PM and ar ( ∆ PMR) = 50 cm2 . Calculate. (a) ar ( ∆ RST ) (b) ar ( □ PMTS)

Solve this:

Q14. In the given figure, 3SR = 2SP ,ST || PM and ar ( $∆$ PMR) = 50 cm² . Calculate.

(a) ar ( $∆$ RST ) (b) ar ( $□$ PMTS)