In ∆PQR , S and T are respectively the points on sides PQ and PR such that PS = 4 cm, QS = 6 cm and QR = 15cm. If ST ll QR then find the length of ST. plz answer as soon as possible
Answers
Answered by
1
Step-by-step explanation:
Hey mate!!
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.
Please mark me brainliest!!
Similar questions