In the figure ST II QR, PQ = 6 cm, PR=9cm,
Ps=2cm then find PT.
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Answer:
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Step-by-step explanation:
Given:
ST∥QR
PT= 4 cm
TR = 4cm
In △PST and △PQR,
∠SPT=∠QPR(Common)
∠PST=∠PQR (Corresponding angles)
△PST∼△PQR(By AA similarity criterion)
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
area△PQR
area△PST
=
PR
2
PT
2
area△PQR
area△PST
=
(PT+TR)
2
4
2
area△PQR
area△PST
=
(4+4)
2
16
=
8
2
16
=
64
16
=
4
1
Thus, the ratio of the areas of △PST and △PQR is
1:4.
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