https://file.aiquickdraw.com/mathbot/file/1729960252392s5fq0ea3.jpg

To solve this problem, we need to determine the length of the rectangle. The key information provided is that the rectangle and the triangle have the same area.

### Step 1: Find the Area of the Triangle
The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

From the image:
- Base of the triangle = 12 cm
- Height of the triangle = 16 cm

\[
\text{Area of the triangle} = \frac{1}{2} \times 12 \times 16 = 96 \text{ cm}^2
\]

### Step 2: Set Up the Area Equation for the Rectangle
The area of a rectangle is calculated by:

\[
\text{Area} = \text{length} \times \text{width}
\]

From the image, the width of the rectangle is given as 7.5 cm. Let the length be \( L \). Since the area of the rectangle is equal to the area of the triangle, we have:

\[
96 = L \times 7.5
\]

### Step 3: Solve for \( L \)

\[
L = \frac{96}{7.5} = 12.8 \text{ cm}
\]

### Conclusion
The length of the rectangle is **12.8 cm**.

Would you like further details or explanations on any part of this solution? Here are some related questions to consider:

1. How do you find the area of different geometric shapes?
2. Can the area formula for triangles be used for any triangle type?
3. What are some real-life applications of calculating the area?
4. How do you convert different units when calculating area?
5. How would the problem change if the triangle were a right triangle with different dimensions?

**Tip:** Always double-check your measurements and units when calculating areas, especially when comparing different shapes.

The rectangle and the triangle have the same area. Work out the length of the rectangle.

Learn how to find the length of a rectangle when it has the same area as a triangle with a base of 12 cm and height of 16 cm. This problem includes geometry concepts and area calculations, suitable for students in Grades 8-10.

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