https://file.aiquickdraw.com/mathbot/file/1726366719815fcavmpih.jpg

Let's analyze and solve the problem in the image.

We are given:
- The dimensions of a rectangular room in a picture are **5 cm by 7 cm**.
- The shorter side of the actual room is **6 m**.
  
We are asked to find:
1. The scale of the picture.
2. The length of the longer side of the actual room.

### Step 1: Find the scale of the picture.
The scale is the ratio between the length in the picture and the actual length of the room. We know the shorter side of the actual room is 6 m, and the shorter side in the picture is 5 cm.

To express both in the same unit, we can convert **6 m to centimeters**:
\[
6 \, \text{m} = 600 \, \text{cm}
\]

Now, the scale is given by:
\[
\text{Scale} = \frac{\text{length in the picture}}{\text{actual length}} = \frac{5 \, \text{cm}}{600 \, \text{cm}} = \frac{1}{120}
\]
So, the scale is **1:120**.

### Step 2: Find the length of the longer side of the actual room.
Now that we know the scale is 1:120, we can use it to find the actual length of the longer side of the room. The length of the longer side in the picture is 7 cm, so the actual length is:
\[
\text{Actual length of the longer side} = 7 \, \text{cm} \times 120 = 840 \, \text{cm}
\]
Convert this to meters:
\[
840 \, \text{cm} = 8.4 \, \text{m}
\]

### Final Answer:
- The scale is **1:120**.
- The actual length of the longer side of the room is **8.4 m**.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you convert between centimeters and meters?
2. What is the formula for finding the scale between two similar objects?
3. Can you calculate the area of the actual room based on these dimensions?
4. How would you find the scale if the actual dimensions were in kilometers?
5. If the dimensions in the picture were doubled, what would be the new scale?

**Tip:** When dealing with scale problems, ensure that both the picture and actual dimensions are in the same units for accurate results.

In a picture, the size of a rectangular room is 5 cm by 7 cm. The shorter side of the actual room is 6 m. What is the scale of the picture and how long is the longer side of the actual room?

Learn how to calculate the scale of a picture based on the size of a rectangular room and the actual room's measurements. The problem involves converting units, applying ratios, and determining the scale factor. Perfect for Grades 5-7.

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