Question

In a right-angled triangle, if the base (Bhuja) is 3 units and the hypotenuse (Karna) is 5 units, what is the value of the perpendicular/altitude (Koti)?

• A. 15
• B. 16
• C. 4
• D. 8

Hint:

This is the most famous Pythagorean triple: (3, 4, 5). If you see 3 and 5 in a right-angled triangle problem, the third side is almost always 4.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The relationship between the sides of a right-angled triangle in Indian mathematics (as described in the Sulba Sutras and later Siddhantas) is identical to the Pythagorean theorem. In Sanskrit terminology:
- Bhuja: The horizontal side (Base).
- Koti: The vertical side (Perpendicular).
- Karna: The diagonal side (Hypotenuse).

Step 2: Key Formula or Approach:
The relationship is expressed as:
\[ \text{Karna}^2 = \text{Bhuja}^2 + \text{Koti}^2 \]
To find the Koti, the formula is rearranged:
\[ \text{Koti} = \sqrt{\text{Karna}^2 - \text{Bhuja}^2} \]

Step 3: Detailed Calculation:
Given values:
- \(\text{Bhuja} (b) = 3\)
- \(\text{Karna} (k) = 5\)
Substituting the values:
\[ \text{Koti} = \sqrt{5^2 - 3^2} \]
\[ \text{Koti} = \sqrt{25 - 9} \]
\[ \text{Koti} = \sqrt{16} \]
\[ \text{Koti} = 4 \]

Step 4: Final Answer:
The value of the Koti (perpendicular) is 4 units.