Math, asked by kashiskummar7888, 11 months ago

In the given figure ps, sq, pt and tr are 4 cm, 1 cm, 6 cm and 15 cm respectively. prove that st parallel to qr. also find the ratio of ar(triangle pst)/ar(trap qrts)

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Answered by knjroopa

Step-by-step explanation:

Given In the given figure ps, sq, pt and tr are 4 cm, 1 cm, 6 cm and 15 cm respectively. prove that st parallel to qr. also find the ratio of ar(triangle pst)/ar(trap qrts)

According to question, From triangle PST and triangle PQR,
PS / PT = 4/6 = 0.67
Also PQ / PR = 5 / 7.5 = 0.67
Now therefore PS/PT = PQ/PR = 0.67
Angle SPT = angle QPR because common angle
So triangle PST = triangle PQR
PS / SQ = PT / TR
4/1 = 6/1.5
4 = 4
Since two points S and T divide the sides in the same ratio, the third side is parallel to ST
So QR is parallel to ST (proved)
Now we need to find the ratio of area of triangle PST / area of triangle RTS
So Area of triangle PST / Area of triangle PQR – Area of triangle PST
= 4^2 / 5^2 – 4^2
= 16 / 25 – 16
Therefore area of triangle PST / Area of triangle RTS = 16 / 9

Reference link will be

https://brainly.in/question/14673968

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Answered by Pagiramdas134

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