The area of rectangle is twice the area of a triangle. The p"rimeter of the rectangle is 58 cm. What is the area of the triangle ?

Options

A. `106 cm^2`
B. `108 cm^2`
C. `104 cm^2`
D. Cannot be determined

Explanation

To solve the problem step by step, we will use the information given about the rectangle and the triangle.

### Step 1: Understand the relationship between the areas
We know that the area of the rectangle (A_rect) is twice the area of the triangle (A_tri). This can be expressed mathematically as:
\[ A_{rect} = 2 \times A_{tri} \]

### Step 2: Use the perimeter of the rectangle
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (L + B) \]
where \( L \) is the length and \( B \) is the breadth of the rectangle. We are given that the perimeter is 58 cm:
\[ 2 \times (L + B) = 58 \]

### Step 3: Simplify the perimeter equation
Dividing both sides of the equation by 2 gives us:
\[ L + B = 29 \]

### Step 4: Express the area of the rectangle
The area of the rectangle can be expressed as:
\[ A_{rect} = L \times B \]

### Step 5: Substitute the area relationship
From Step 1, we know:
\[ A_{rect} = 2 \times A_{tri} \]
Thus, we can write:
\[ L \times B = 2 \times A_{tri} \]

### Step 6: Find the area of the triangle
To find the area of the triangle, we need to express it in terms of the rectangle's area:
\[ A_{tri} = \frac{L \times B}{2} \]

### Step 7: Determine the values of L and B
Since we only know that \( L + B = 29 \) and we do not have specific values for \( L \) and \( B \), we cannot determine a unique area for the triangle. The area of the triangle depends on the specific values of \( L \) and \( B \).

### Conclusion
Since we cannot determine the specific dimensions of the rectangle, we cannot find a unique area for the triangle. Therefore, the area of the triangle cannot be determined with the given information.

### Final Answer
The area of the triangle cannot be determined.

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