Mai wants to make a scale drawing of her kitchen. Her kitchen is a rectangle with length 6m and width 2m. She decides on a scale of 1 to 40 . a. Draw and label the dimensians of a scale drawing of Mai’s kitchen, using a scale of 1 to 40 .
The Correct Answer and Explanation is :
To create a scale drawing of Mai’s kitchen using a scale of 1 to 40, we first need to understand how the scale works. A scale of 1 to 40 means that 1 unit on the drawing represents 40 units in reality. In other words, if an object measures 40 meters in real life, it would only measure 1 meter on the scale drawing.
Step 1: Calculate the dimensions of the scale drawing
Mai’s kitchen has the following real-life dimensions:
- Length: 6 meters
- Width: 2 meters
To convert these dimensions into the scale drawing:
- Scale for length:
Divide the actual length (6 meters) by 40: 640=0.15 meters (or 15 cm)\frac{6}{40} = 0.15 \text{ meters} \text{ (or 15 cm)} - Scale for width:
Divide the actual width (2 meters) by 40: 240=0.05 meters (or 5 cm)\frac{2}{40} = 0.05 \text{ meters} \text{ (or 5 cm)}
Step 2: Draw the scale diagram
Now, we can draw a rectangle with the dimensions of 15 cm (length) by 5 cm (width), based on the scale of 1:40.
Step 3: Label the dimensions
- The length of the rectangle on the scale drawing is 15 cm.
- The width of the rectangle on the scale drawing is 5 cm.
The kitchen’s scale drawing will be a smaller version of the real kitchen, showing the reduced dimensions on paper but maintaining the same proportions as the real-life kitchen.
Explanation of the process
To create a scale drawing, we use the scale factor to reduce the dimensions proportionally. This means that every 1 cm on the paper represents 40 cm (or 0.4 meters) in the real world. For Mai’s kitchen, the 6-meter length becomes 15 cm, and the 2-meter width becomes 5 cm on the drawing. This allows her to visualize her kitchen on a smaller scale while maintaining accurate proportions.