Question

PQR is a right-angled triangle with the right angle at Q and k being the length of the perpendicular from
Q on PR. If I m and n are the lengths of sides PQ, QR, and PR respectively, then which of the following
holds true?​

Answer 1

Answer:

In triangles PQS and PQR

∠P is common to both.

and ∠PSQ=∠PQR

Triangles PQS and PQR are equiangular

∴

PQ

PS

=

QR

QS

or, PS=

QR

PQ⋅QS

...(i)

Again, triangles QRS and PQR are equiangular

∴

QR

SR

=

PQ

QS

or, SR=

PQ

QS⋅QR

...(ii)

From eqns. (i) and (ii)

SR

PS

=

QR

PQ⋅QS

⋅

QR⋅QS

PQ

=

QR

2

PQ

2

I hope it is helpful for you