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Q.

In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6cm such that the segments QT and TR, into which QR is divided by the point of contact T are of lengths 12 cm and 9 cm respectively, PS and PU measures $x$ cm . If the area of $∆ PQR = 189 {cm}^{2}$ then, which of the following is the length of side PQ?

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a

17.5 cm

b

20 cm

c

22.5 cm

d

25 cm

answer is C.

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Detailed Solution

Consider the given figure,
Question Image

Question Image

Given that PS = x cm, QT = 12cm, QS = 12cm, RT = 9cm, RU = 9cm, Radius = OU = OS = OT = 6cm.
We know that,
Area of the triangle

= 12 × b a s e × h e i g h t

From figure,
Question Image

Question Image

Simplifying,

⇒ 2 x = 21 ⇒ x = 10.5 c m

The value of PQ,

PQ = Q S + S P

⇒ P Q = 12 + 10.5

⇒ P Q = 22.5 cm

Hence, the value of PQ is 22.5 cm.
Therefore, option 3 is correct.

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In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6cm such that the segments QT and TR, into which QR is divided by the point of contact T are of lengths 12 cm and 9 cm respectively, PS and PU measures x cm . If the area of ∆PQR=189cm2 then, which of the following is the length of side PQ?