The rectangular frame for a picture is 24.5 cm wide and 32.6 cm high . The border is 3.4 cm wide. Calculate the perimeter of the picture.

Answer

To solve the problem step by step, we need to calculate the dimensions of the picture inside the frame and then find the perimeter of that picture.

### Step 1: Understand the dimensions of the frame and border
The frame has the following dimensions:
- Width of the frame: 24.5 cm
- Height of the frame: 32.6 cm
- Width of the border: 3.4 cm

### Step 2: Calculate the dimensions of the picture
Since the border is present on all sides of the picture, we need to subtract the width of the border from both the width and height of the frame.

1. **Calculate the width of the picture:**
\[ \text{Width of the picture} = \text{Width of the frame} - 2 \times \text{Width of the border} \]
\[ \text{Width of the picture} = 24.5 \, \text{cm} - 2 \times 3.4 \, \text{cm} \]
\[ \text{Width of the picture} = 24.5 \, \text{cm} - 6.8 \, \text{cm} = 17.7 \, \text{cm} \]

2. **Calculate the height of the picture:**
\[ \text{Height of the picture} = \text{Height of the frame} - 2 \times \text{Width of the border} \]
\[ \text{Height of the picture} = 32.6 \, \text{cm} - 2 \times 3.4 \, \text{cm} \]
\[ \text{Height of the picture} = 32.6 \, \text{cm} - 6.8 \, \text{cm} = 25.8 \, \text{cm} \]

### Step 3: Calculate the perimeter of the picture
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
Here, we will use the calculated dimensions:
- Length (Height of the picture) = 25.8 cm
- Width (Width of the picture) = 17.7 cm

Substituting the values:
\[ P = 2 \times (25.8 \, \text{cm} + 17.7 \, \text{cm}) \]
\[ P = 2 \times 43.5 \, \text{cm} = 87 \, \text{cm} \]

### Final Answer
The perimeter of the picture is **87 cm**.

---