Question

Column A: The area of the triangular region
Column B: 6

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

For a right-angled triangle, the two legs are always the base and height. The longest side, the hypotenuse, is not used in the basic area calculation. The numbers (3, 4, 5) form a common Pythagorean triple.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to calculate the area of the triangle shown in the diagram.
Step 2: Key Formula or Approach:
The diagram shows a right-angled triangle, indicated by the square symbol at one of the vertices. The area of a right-angled triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] The base and height are the lengths of the two sides that form the right angle (the legs).
Step 3: Detailed Explanation:
Column A: From the diagram, the lengths of the legs of the right-angled triangle are 3 and 4. The side with length 5 is the hypotenuse.
Using the area formula: \[ \text{Area} = \frac{1}{2} \times 3 \times 4 \] \[ \text{Area} = \frac{1}{2} \times 12 = 6 \] So, the quantity in Column A is 6.
Column B: The quantity is 6.
Comparison: Column A is 6, and Column B is 6. The two quantities are equal.
Step 4: Final Answer:
The area of the given triangle is 6, which is equal to the quantity in Column B.