Question 5 In given figure, ST RQ, PS = 3 cm and SR = 4 cm. Find the ratio of the area of PST to the area of PRQ.
Given: ABC
ST II RQ
PS = 3 cm, SR = 4cm
To find : ( )/( )
Proof:
In PRQ & PST,
QPR = TPS
PRQ = PST
PRQ ~ PST
Now,
we know that in similar triangles,
Ratio of area of triangle is equal to ratio of square of corresponding sides
( )/( )=( / )^2
( )/( )=( /( + ))^2
( )/( )=(3/(3 + 4))^2
( )/( )=(3/7)^2
( )/( )=9/49
Required Ratio = 9 : 49
(Putting PS = 3 cm,
SR = 4 cm)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.