CMAT 2021 Solved Question Paper

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Question : 17 of 100

Marks: +1, -0

In triangle PQR, PS is perpendicular to QR and S divides

\Q \R

in the ratio of

3: 1

internally. If

{\PQ}=21

and

{\PR}=9

, find

{\QR}

.

$18 \√{5}$
$16 \√{5}$
$15 \√{5}$
$12 \√{5}$

Solution:

Given

Let QS and SR be

3 x

and

1 x

units respectively. In ΔPQS and

\Δ\P \R \S, \P \S

is common
∴

\√{(21)^{2}-(3 x)^{2}}=\√{(9)^{2}-(x)^{2}}

[∵Pythagoras theorem]

441-9 x^{2}=81-x^{2}

x=\√{45}=3 \√{5}

∴

\Q \R=4 x=4 ×3 ×\√{5}=12 \√{5}

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