What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units?

Options

A. lw/2
B. lw/3
C. lw/6
D. lw/4

Answer

To find the area of the largest triangle that can be fitted into a rectangle of length \( l \) units and width \( w \) units, we can follow these steps:

### Step 1: Understand the dimensions of the rectangle
We have a rectangle with:
- Length = \( l \)
- Width = \( w \)

### Step 2: Identify the triangle configuration
The largest triangle that can fit inside the rectangle will have its base along one side of the rectangle and its height extending to the opposite side. A right triangle is the best configuration for maximizing area in this case.

### Step 3: Determine the base and height of the triangle
- **Base** of the triangle can be taken as the length of the rectangle, which is \( l \).
- **Height** of the triangle can be taken as the width of the rectangle, which is \( w \).

### Step 4: Use the area formula for a triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

### Step 5: Substitute the values of base and height
Substituting the values of base and height into the area formula:
\[ A = \frac{1}{2} \times l \times w \]

### Step 6: Simplify the expression
Thus, the area of the largest triangle that can be fitted into the rectangle is:
\[ A = \frac{lw}{2} \]

### Final Answer
The area of the largest triangle that can be fitted into a rectangle of length \( l \) units and width \( w \) units is:
\[ \frac{lw}{2} \text{ square units} \]

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