In , the sides are , and . Point is chosen on so that . The line drawn through meets…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

In

\Delta PQR

, the sides are

PQ = 30\,\text{cm}

,

PR = 40\,\text{cm}

and

QR = 50\,\text{cm}

. Point

S

is chosen on

PQ

so that

PS = 18\,\text{cm}

. The line

ST

drawn through

S

meets

PR

at

T

with

ST \parallel QR

. Point

U

is taken on

PS

so that

PU = 12\,\text{cm}

. The line

UV

drawn through

U

meets

PT

at

V

with

UV \parallel QR

. (a) Show that

\Delta PST

is similar to

\Delta PQR

and hence find

PT

. (b) Show that

\Delta PUV

is similar to

\Delta PST

and hence find

PV

. (c) Find the ratio of the area of

\Delta PUV

to the area of

\Delta PQR

.

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