Class 11

Math

Algebra

Sequences and Series

A right triangle is drawn in a semicircle of radius $21 $ with one of its legs along the diameter. The maximum area of the triangle is

- $41 $
- $3233 $
- $1633 $
- $81 $

Since, its one side is along the diameter

Therefore, diameter is the hypotenuse of the triangle ....[ prop. of semicircle]

let $a$ & $b$ be the other sides of the triangle

Therefore, $a_{2}+b_{2}=(2r)_{2}=1$

We know that A.M$≥$G.M

so $2a_{2}+b_{2} ≥a_{2}b_{2} =ab$

$⇒ab≤21 $

Area of right angled triangle $2ab ≤41 $