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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. - Geometry

MCQ

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.

Concept: Apollonius Theorem
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APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 2 Pythagoras Theorem
Problem Set 2 | Q 1.6 | Page 43
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