Question

In a $△ABC$, if $a=18cm,b=24cm$ and $c=30cm$ then $R=$

• A. $16cm$
• B. $15cm$
• C. $24cm$
• D. $30cm$

Answer 1

The correct option is B $15cm$

In $△ABC,a=18cm,b=24cm,c=30cm$

here $a^2+b^2={18}^2+{24}^2=900$ and $c^2={30}^2=900⟹c^2=a^2+b^2$

$⟹△ABC$ is a right angled triangle with hypotenuse as $c$

as we know that in right angled triangle ,hypotenuse will be 2 times of radius of circumcircle ,i.e. $c=2R$

$⟹R=\frac{c}{2}$

$⟹R=\frac{30}{2}=15cm$