Question

Triangle ABC is a right angled triangle, right angled at B. If lengths of AB and BC are 60 cm and 80 cm respectively, and BD is an altitude of triangle ABC, then find the length of AD in cm.

• A. 34
• B. 36
• C. 40
• D. 42

Hint:

In right triangle with altitude: - $AB^2 = AD \cdot AC$ - Very useful shortcut for such problems

Answer 1

The Correct Option is B

Concept: In a right-angled triangle, when altitude is drawn from the right angle to the hypotenuse:
• $AB^2 = AD \cdot AC$
• $BC^2 = DC \cdot AC$

Step 1: Find hypotenuse.
\[ AC = \sqrt{AB^2 + BC^2} = \sqrt{60^2 + 80^2} = \sqrt{3600 + 6400} = \sqrt{10000} = 100 \]

Step 2: Use relation.
\[ AB^2 = AD \cdot AC \] \[ 60^2 = AD \cdot 100 \] \[ 3600 = 100 \cdot AD \]

Step 3: Solve for AD.
\[ AD = \frac{3600}{100} = 36 \]

Step 4: Final conclusion.
Thus, the length of $AD$ is: \[ 36 cm \]