https://file.aiquickdraw.com/mathbot/file/1730539310750jvnlmknc.jpg

To find the perimeter of the entire figure formed by the overlapping rectangles, let's analyze the shape and calculate it step-by-step.

### Step 1: Understanding the Shape
The figure consists of two overlapping rectangles, with dimensions provided for one of them: a height of \( 15 \, \text{m} \) and a width of \( 20 \, \text{m} \).

### Step 2: Identifying the Perimeter
The perimeter of a figure is the total length around the shape. Since this figure has overlapping parts, we need to count only the outer edges and ignore the overlapping internal edges.

#### Observations
1. The base of the larger rectangle (20 m) forms part of the perimeter.
2. The height of 15 m extends vertically.
3. Due to the overlapping area, there are additional slanted edges on the left side of the figure.

### Step 3: Calculating Slanted Edges (Using Pythagoras' Theorem)
The two triangles on the sides are right triangles, so we can calculate the lengths of these slanted edges using the Pythagorean theorem.

1. **Right Triangle on the Left Side:**
   - Hypotenuse \( = \sqrt{(15^2 + 20^2)} = \sqrt{225 + 400} = \sqrt{625} = 25 \, \text{m} \).

2. **Right Triangle on the Right Side:**
   - Hypotenuse \( = \sqrt{(15^2 + 20^2)} = 25 \, \text{m} \).

### Step 4: Adding All Outer Edges
To find the perimeter, we add up all the unique outer edges:

\[
\text{Perimeter} = 20 + 15 + 25 + 20 + 15 + 25 = 90 \, \text{m}
\]

### Conclusion
The perimeter of the entire figure is **90 meters**.

### Answer
**(B) 90 m**

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Would you like further details on this solution or have any questions?

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Here are some related questions:
1. How can we calculate the area of the overlapping figure?
2. What happens to the perimeter if the rectangles were not overlapping?
3. How would the solution change if one side of the rectangle were unknown?
4. What if the shape were composed of more than two overlapping rectangles?
5. How can we calculate perimeters for irregular shapes in general?

**Tip:** When dealing with overlapping shapes, remember to exclude shared edges from perimeter calculations.

Given two rectangles overlapping as below, find the perimeter of the whole figure.

Calculate the perimeter of a figure formed by two overlapping rectangles with dimensions 15 m and 20 m. This problem involves geometry, perimeter calculation, and the Pythagorean theorem. Ideal for students in Grades 9-10.

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