Each question is followed by two statements, I and II. Answer each que...
The question cannot be answered using either of the statements alone. We need not combine the statements as statement II implies statement I.
Answer: 5
Hence Option 5
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Each question is followed by two statements, I and II. Answer each que...
Answer:
The area of a triangle can be calculated using various formulas depending on the given information. In this case, we are given two statements and we need to determine if either statement or both statements together can help us find the area of the triangle.
Statement I: The measures of the sides of the triangle are in arithmetic progression.
Statement II: The ratio of the sides is 2 : 3 : 4.
Let's analyze each statement separately:
Statement I alone:
If the measures of the sides of the triangle are in arithmetic progression, it means that the lengths of the sides can be represented as a, a + d, and a + 2d, where a is the first term and d is the common difference. However, this information alone is not sufficient to determine the area of the triangle. The area of a triangle depends on the lengths of its sides as well as the angles formed by these sides.
Statement II alone:
If the ratio of the sides is 2:3:4, it means that the lengths of the sides can be represented as 2x, 3x, and 4x, where x is a constant. This information alone is also not sufficient to determine the area of the triangle. As mentioned earlier, the area of a triangle depends on the lengths of its sides as well as the angles formed by these sides.
Both statements together:
Combining both statements, we know that the lengths of the sides can be represented as a, a + d, and a + 2d, as well as 2x, 3x, and 4x. However, this still does not provide enough information to calculate the area of the triangle. We need additional information such as the height or one of the angles to calculate the area.
Therefore, neither statement alone nor both statements together provide enough information to determine the area of the triangle. Hence, the correct answer is option 'E' - Mark (5).
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