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Maths-

General

Easy

Question

In triangle $A B C$ if angle $C$ is $90 degree$ and area of triangle is 30 sq. units, then the minimum possible value of the hypotenuse $c$ is equal to

$30 \sqrt{2}$
$60 \sqrt{2}$
$120 \sqrt{2}$
$\sqrt{30}$

The correct answer is: $square root of 30$

$increment equals fraction numerator 1 over denominator 2 end fraction a b rightwards double arrow a b equals 60$
$b equals c cos invisible function application theta comma blank a equals c sin invisible function application theta$
$rightwards double arrow increment equals fraction numerator 1 over denominator 2 end fraction c to the power of 2 end exponent sin invisible function application theta cos invisible function application theta equals fraction numerator c to the power of 2 end exponent sin invisible function application 2 theta over denominator 4 end fraction equals 30$
$rightwards double arrow c to the power of 2 end exponent equals 120 blank c o s e c blank 2 theta$
$rightwards double arrow c to the power of 2 end exponent blank subscript m i n end subscript equals 120$
$rightwards double arrow c subscript m i n end subscript equals 2 square root of 30$

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