{\PQR} is a triangle. {\S} is a point on the side {\QR} of \triangle {\PQR} such that \angle {\PSR}=\angle {\QPR}. Given {\QP}=8 {\cm}, {\PR}=6 {\cm} and {\SR}=3 {\cm} (i) Prove \triangle {\PQR} ∼ \triangle {\SPR} (ii) Find the length of Q R and PS (iii) {\text{ area of } \triangle P Q R}/{\text{ area of } \triangle S P R}

ICSE Class X Math 2017 Solved Paper - Question 30

Question : 30 of 31

Marks: +1, -0

{\PQR}

is a triangle.

{\S}

is a point on the side

{\QR}

△ {\PQR}

such that

∠ {\PSR}=∠ {\QPR}

.
Given

{\QP}=8 {\cm}, {\PR}=6 {\cm}

and

{\SR}=3 {\cm}

(i) Prove

△ {\PQR} ∼ △ {\SPR}

(ii) Find the length of

Q R

and PS
(iii)

\;{\;\text " area of "\; △ P Q R}/{\;\text " area of "\; △ S P R}

Solution:

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