Question

Irrgiven figure PS and PT are tangents if ps=14 c.m. then Perimeter of triangle
PQR is,
​

Answer 1

Explanation:

Correct option is A)

From the figure in the question,

As PQRT is a parallelogram

QR=PT=5cm

Given, PS=14cm

PS=PT+TS

⇒14=5+TS

∴TS=9cm

From △PQR; By Pythogoras Theorem

PQ

2

=PR

2

=QR

2

PQ=

13

2

−5

2

=12cm

⇒PQ=TR=12cm [opposite of parallelogram are equal]

∴ from △STR

tana=

9

12

=

3

4

Answer 2

Complete Question:

In above figure, if PS=14 cm, then the perimeter of triangle PQR is equal to:

Answer:

The answer is 30 cm.

Explanation:

In given figure,

Given data:

$l(PR) = 13 cm\\l(QR) = 5 cm$

ΔPQR is a right angle triangle.

Hence,

Using Pythagoras theorem:

$l(PR)^{2} = l(QR)^2 + l(PQ)^2\\13^2 = 5^2 + l(PQ)^2\\169 = 25 + l(PQ)^2\\l(PQ)^2 = 169 - 25$

$l(PQ)^2 = 144\\l(PQ) = \sqrt{144} \\l(PQ) = 12 cm$

Hence,

Perimeter of ΔPQR = $l(PQ) + l(QR) + l(PR)$

= 12 + 5 + 13

= 30 cm.

Hence, Perimeter of ΔPQR = 30 cm.

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