Question

Δabc is a right angled triangle, the radius of its circumcircle is 3 cm and the length of its altitude drawn from the opposite vertex to the hypotenuse is 2 cm. then the area of the triangle is

Answer 1

Let ABC be the right angled triangle right angled at B.Let O be the centre of circle. O is the mid point of hypotenuse by geometry

OA= OB = OC = radius of the circumcircle = 3 cm

Hypotenuse AC= Diameter of circle =2 × radius of circumcircle=2×3=6 cm

Let be the perpendicular from B on AC

BM = 2 cm

area of right angle ∆= 1/2 ×B×H

=1/2×6×2 = 6 cm²

Answer 2

$\\ \boxed{ \rm \: let \: \triangle \: abc \: be \: right \: angled \: at \: B}$

$\textsf{Then hypotenus \: AC = diameter \: of \: its \: circumcircle}$

$\textsf{ = (2 × 3) = 6cm}$

$\textsf{Let BL⏊AC .Then,BL=2cm}$

$\textsf{Area of triangle ABC}= \rm \huge {\frac{1}{2}} \small ×AC×BL$

$\rm = \large \big( \frac{1}{2} \times 3 \times 2 \big)cm {}^{2} = 6cm {}^{2}$