Question

In the figure, ST||QR, PS = 3 cm, SR = 4 cm, find the ratio of area ∆PST to area of ∆PRQ

Answer 1

Answer:

Step-by-step explanation:

PS = 3 cm

SR = 4 cm

PR = 3+4 = 7 cm

In PTS n PQR,

angle TPS = angle QPR

ST||QR

So, PS/PR = PT/ PQ

So by SAS PTS is similar to PQS

So,

Area of PST/Area of PRQ = square of PS/ square of PR

                                          = 9/49

Hence the ratio is 9:49

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