Question

If the area of the largest triangle that can be inscribed in a semi-circle whose radius is r is :

• A. $r^2$
• B. $r^3$
• C. $2r^2$
• D. $2r^3$

Answer 1

The correct option is A $r^2$

When a triangle is inscribed in a semi-circle, its maximum height can be $r$.

And for area which is equal to $\frac{1}{2}\left(base\right)\left(height\right),$ we need to maximize the base.

So far maximum area we take diameter as base.

Hence maximum area =$\frac{1}{2}\left(base\right)\left(height\right)=\left(1/2\right)\left(r\right)\left(2r\right)=r^2$.