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

Answer: Option A

Let the sides be a cm and 2a cm

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