SSC CHSL 6 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

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Question : 56 of 100

Marks: +1, -0

In

△ P Q R

, points

T

and

S

are on

P Q

and

P R

, respectively, such that

T S

is parallel to

Q R

. If

T Q=7.2 {cm}

,

P S=1.8 {cm}

and

S R=5.4 {cm}

, then find the length of

P T

.

$2 {cm}$
$2.4 {cm}$
$1.35 {cm}$
$3.6 {cm}$

Solution:

Given,

Since,

∠ P

is common and

T S \| Q R

,

∴ \;\; △ P T S ∼ △ P Q R

∴ \;\; \;{P T}/{P Q}=\;{P S}/{P R}

⇒ \;\; P T=\;{P S}/{P R} × P Q=\;{P S}/{P R} ×(P T+T Q)

⇒ \;\; P T=\;{1.8}/{72} ×(P T+72)

⇒ \;\; 7.2 P T=1.8 P T+1.8 × 7.2

⇒ \;\; 7.2 P T-1.8 P T=1.8 × 7.2

⇒ \;\; \;\; 5.4 P T=1.8 × 7.2

⇒ \;\; P T=\;{1.8 × 7.2}/{5.4}=2.4 {cm}

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