#### Question

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

#### Solution

We know that,

In a right angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex, is the geometric mean of the segments into which the hypotenuse is divided.

\[\therefore {AD}^2 = CD \times DB\]

\[ = 4 \times 9\]

\[ = 36\]

\[ \Rightarrow AD = 6 cm\]

Hence, the correct option is 6 cm.

Is there an error in this question or solution?

Solution Some Question and Their Alternative Answer Are Given. 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. Concept: Apollonius Theorem.