One side of a right-angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is :

Solution (By Examveda Team)

Let the sides be a cm and 2a cm

Then,
$$\eqalign{ & {a^2} + {\left( {2a} \right)^2} = {\left( {10} \right)^2} \cr & \Rightarrow 5{a^2} = 100 \cr & \Rightarrow {a^2} = 20 \cr} $$
∴ Area :
$$\eqalign{ & = \left( {\frac{1}{2} \times a \times 2a} \right) \cr & = {a^2} \cr & = 20\,c{m^2} \cr} $$