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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.
Options
9 cm
4 cm
6 cm
\[2\sqrt{6}\] cm
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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.
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