question_answer

The area of the largest triangle that can be inscribed in a semicircle of radius 21 is: (CBSE 2017)

A) \[221\,c{{m}^{2}}\]

B) \[331\,c{{m}^{2}}\]

C) \[441\,c{{m}^{2}}\]

D) \[555\,c{{m}^{2}}\]

Correct Answer: C

Solution :

[c] Let \[\Delta ABC\] be the largest triangle.

Given, radius of semicircle

\[=OA=OB=OC=21\,cm\]

Area of \[\Delta ABC=\frac{1}{2}\times BC\times AQ\]

\[=\frac{1}{2}\times (21+21)\times 21\]

\[=\frac{1}{2}\times 42\times 21=441\,c{{m}^{2}}\]

Hence, the area of required triangle is \[441c{{m}^{2}}\]