The area of a right-angled triangle is 20 sq.cm and one of the sides containing the right angle is 4 cm. The altitude on the hypotenuse is :

Answer: Option D

Let the length of the other side containing the right angle be x cm
Then,
$$\begin{array}{rl}& \frac{1}{2}\times 4\times x=20\\ & \Rightarrow x=10\text{ cm}\end{array}$$
Hypotenuse :
$$\begin{array}{rl}& =\sqrt{{10}^2+4^2}\text{ cm}\\ & =\sqrt{116}\text{ cm}\\ & =2\sqrt{29}\text{cm}\end{array}$$
Let the altitude on the hypotenuse be h cm
Then,
$$\begin{array}{rl}& \frac{1}{2}\times 2\sqrt{29}\times h=20\\ & \Rightarrow h=\frac{20}{\sqrt{29}}\text{ cm}\end{array}$$