Two right-angled triangles share a common vertex (Q )

MATHEMATICS · Subjective · CBSE · Mathematics · The Baudhayana-Pythagoras Theorem · The Baudhayana-Pythagoras Theorem

Problem

Two right-angled triangles share a common vertex

Q

. In

\triangle PQR

right-angled at

Q

, the known side lengths are

PQ = 9\;\text{cm}

and

QR = 12\;\text{cm}

. In another right-angled triangle

QRS

also right-angled at

Q

, the hypotenuse is

QS = 15\;\text{cm}

. (i) Find the length

PR

. (ii) Determine the length

RS

. (iii) The points

P, R, S, Q

in that order form a quadrilateral. Calculate its perimeter.