Sol:

Base of the right angled triangle is 'b' units.

Area of the right angled triangle is "A' sq units.

A = 1/2 × b × h

⇒ h = 2A / b

Another side of the right angled triangle containing the right angle = 2A / b

Hypotenuse of the right angled triangle according to Pythagoras theorem:

(Hypotenuse)^{2} = (b)^{2} + (2A / b)^{2}

⇒ (Hypotenuse)^{2} = b^{2} + (4A^{2} / b^{2})

⇒ Hypotenuse = √[b^{2} + (4A^{2} / b^{2})]

⇒ Hypotenuse = √[(b^{4} + 4A^{2}) / b^{2}]

⇒ Hypotenuse = 1/b √[(b^{4} + 4A^{2})]

Area of the right angle considering hypotenuse as the base.

A = 1/2 × 1/b √[(b^{4} + 4A^{2})] × altitude on hypotenuse

⇒ 2A = 1/b √[(b^{4} + 4A^{2})] × altitude on hypotenuse

⇒ 2Ab = √[(b^{4} + 4A^{2})] × altitude on hypotenuse

⇒ Altitude on hypotenuse = 2Ab / √[(b^{4} + 4A^{2})]

Therefore, length of the altitude on hypotenuse of the right angled triangle is 2Ab / √[(b^{4} + 4A^{2})].