SSC CGL Tier II 21 Sep 2014 Paper

Question : 14 of 100

Marks: +1, -0

a and b are two sides adjacent to the right angle of a rightangled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then

p^ 2

is equal to

$a^{2}+b^{2}$
${1}/{a^{2}}+ {1}/{b^{2}}$
${a^{2} b^{2}}/{a^{2}+b^{2}}$
$a^{2}-b^{2}$

Validate

Solution:

(3)

BD ⊥ AC
AB ⊥ BC
Hypotenuse of ΔABC

=√{A B^{2}+B C^{2}}

=√{a^{2}+b^{2}}

Area of

\Δ{\ABC}= {1}/{2} ×{AB} ×{BC}

= {1}/{2} ×{AC} ×{BD}

⇒{AB}×{BC}= {AC} ×{BD}

⇒ a b=√{a^{2}+b^{2}}× p

On squaring both sides,

a^{2} b^{2} = (a^{2}+b^{2} ) p^{2}

∴ p^{2} = {a^{2} b^{2}}/{a^{2}+b^{2}}

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