Question

If ST||RQ,PS=3 cm and SR=4cm. find the ratio of the area of triangle PST to the area of triangle triangle PRQ

Answer 1

since ST || RQ
therefore
PS/SR =PT/TQ (By thales theorem)
in triangle PST and PRQ
PS/SR=PT/TQ (proved above)
angle P= angle P (common)
therefore, by SAS Triangle PST ~ PRQ
ar (PST)/ar (PRQ)=(PS/SR)^2
=> (3/4)^2
=>9/16

Answer 2

Answer:

9:49

Step-by-step explanation:

Given

ST || RQ

PS= 3 cm

SR = 4cm

Proof :--

ar(∆PST) /ar(∆PRQ) = (PS)²/(PR)²

ar(∆PST) /ar(∆PRQ) = 3²/(PS+SR)²

ar(∆PST) /ar(∆PRQ) = 9/(3+4)²= 9/7² = 9/49

Hence, the required ratio ar(∆PST) :ar(∆PRQ) = 9:49