Some question and their alternative answer are given. Select the correct alternative. Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude. 9 cm 4 cm 6 cm \[2\sqrt{6}\] cm

Explanation:- 

Let the altitude be ‘h’ and the hypotenuse be ‘c’, and the two parts of the hypotenuse be ‘a’ and ‘b’, such that ‘a’ is adjacent to the leg of length 4 cm and ‘b’ is adjacent to the leg of length 9 cm.

According to the Pythagorean theorem,

c^2 = a^2 + h^2 …(1) c^2 = b^2 + h^2 …(2)

From the given information, we know that a + b = c. Substituting this in equations (1) and (2) and simplifying, we get:

h = ab/c

Substituting a + b = c, we get:

h = ab/(a+b)

Substituting the given lengths, we get:

h = (4 × 9)/(4 + 9) = 36/13

Therefore, the length of the altitude is approximately 2.77 cm (rounded to two decimal places).

The closest option is [2\sqrt{6}] cm, but this is not equal to the exact value of the altitude. Therefore, the correct answer is none of the given options.