Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question.
What is the area of right angled trangle ?
(A) The perimeter of a triangle is 30 cm.
(B) The ratio between the base and the height of the triangle is 5:12.
(C ) The area of the triangle is equal to the area of a rectangle of length 10 cm.

Options

A. Only B and C
B. Only A and B
C. Only either A or B and C
D. Only A and C

Answer

To find the area of a right-angled triangle, we can use the formula:

\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

Now, let's analyze the statements provided to determine which ones are necessary to answer the question.

### Step 1: Analyze Statement A
**Statement A:** The perimeter of a triangle is 30 cm.

- The perimeter of a triangle is the sum of all its sides. However, knowing the perimeter alone does not provide us with the base and height of the triangle directly. Therefore, this statement is not sufficient to find the area.

### Step 2: Analyze Statement B
**Statement B:** The ratio between the base and the height of the triangle is 5:12.

- This statement gives us a relationship between the base and height. If we let the base be \(5x\) and the height be \(12x\), we can use this information in the area formula. However, we still need a specific value for either the base or height to calculate the area.

### Step 3: Analyze Statement C
**Statement C:** The area of the triangle is equal to the area of a rectangle of length 10 cm.

- This statement tells us that the area of the triangle is equal to the area of a rectangle with a length of 10 cm. Since the area of a rectangle is calculated as length times breadth, we can express the area of the triangle in terms of the rectangle's area. However, we still need to know the breadth of the rectangle to use this information effectively.

### Conclusion
To find the area of the triangle, we need both the ratio of the base and height (from Statement B) and the area of the triangle (from Statement C). Therefore, both statements B and C are necessary to answer the question.

### Final Answer:
The necessary statements to answer the question are **B and C**.

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