Read the question and statements provided and decide whether the data provided in the statements are sufficient to answer the question.
Question: Find the area of a triangle.
Statements:
I. One of its sides is .
II. It is an equilateral triangle.
- ABoth Statements I and II are required
- BOnly Statement II is sufficient
- CNeither Statement I nor II is sufficient
- DOnly Statement I is sufficient
Solution & Step-by-step Explanation
To find the area of a triangle, we need specific dimensions.
* Statement I alone tells us only one side is , which is not sufficient because the triangle could have any shape.
* Statement II alone tells us it is an equilateral triangle, but without a specific side length, we cannot calculate the exact numerical area.
* Combining Statement I and Statement II: Since it is an equilateral triangle and one side is , all three sides must be . The area can now be calculated using the formula:
Thus, both statements together are required to answer the question.
* Statement I alone tells us only one side is , which is not sufficient because the triangle could have any shape.
* Statement II alone tells us it is an equilateral triangle, but without a specific side length, we cannot calculate the exact numerical area.
* Combining Statement I and Statement II: Since it is an equilateral triangle and one side is , all three sides must be . The area can now be calculated using the formula:
Thus, both statements together are required to answer the question.