QJEEM22Ma8b5a: JEE Main 2022 Mathematics - Class 11 JEEM22Ma8b5a Solution: Let R be the point (3, 7) and let P and Q be two points on the…

Let, side of triangle = a.

$h = {{|3 + 7 - 5|} \over {\sqrt {{1^2} + {1^2}} }}$

$= {5 \over {\sqrt 2 }}$

From figure, $h = a\sin 60^\circ$

$\Rightarrow a = {{2h} \over {\sqrt 3 }}$

$= {2 \over {\sqrt 3 }} \times {5 \over {\sqrt 2 }}$

$= {{10} \over {\sqrt 6 }}$

$\therefore$ Area $= {3 \over 4}{\left( {{{10} \over {\sqrt 6 }}} \right)^2}$

$= {{25} \over {2\sqrt 3 }}$