Question

in the triangle PQR, the point S divides the line PQ in the ratio 1:3, and T divides the line RQ in the ratio 3:2.

PR =a and PQ =b

express the following in terms of a and b

PS , SR, and TQ

Answer 1

SOLN :

Let's illustrate thetriangle as follows :

It is given that PQ = b

Also PQ = PS + SQ................(1)

It is given S divides PQ in the ratio 1:3

So SQ /PS= 1/3

      SQ= ....................(2)

Substituting (2) in (1),

PQ =

then, PS = ............(3)

Substituting (3) in (2),

SQ =

It is given that PR = a

By Pythagores theorem,

Now T divides RQ in the ratio 3:2

RQ = RT+TQ.............(4)

AND TQ/RT = 3:2

TQ = ............(5)

Substituting (5) in (4),

THEN,

NOW,

By Pythagores theorem,

HENCE,