Xavier Aptitude Test 2011 Paper

Question : 59 of 101

Marks: +1, -0

In a city, there is a circular park. There are four points of entry into the park, namely P, Q, R and S. Three paths were constructed which connected the points PQ, RS and PS. The length of the path PQ is 10 units and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units and it was found that the angle PTS is 60°. Find the area (in square units) enclosed by the paths PT, TS and PS. (2 marks)

$36√ 3$
$54 √3$
$72 √3$
$90 √3$
None of the above

Validate

Solution:

= {area}

\Δ{PTS}=\ {1}/{2}(\ {PT})( {SU})

=\ {1}/{2}(18) \ {\√{3}}/{2}(16)=72 \√{3}

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