Kathleen measured a house and its lot and made a scale drawing. The scale of the drawing was 4 centimeters : 3 meters. The actual length of the front patio is 24 meters. How long is the patio in the drawing?

centimeters

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

To convert the actual length of the front patio to the length in the drawing using the given scale, you can set up a proportion based on the scale provided.

The scale of the drawing is 4 centimeters for every 3 meters.

  1. Set up the proportion using the actual length of the patio. \[ \frac{4 \text{ cm}}{3 \text{ m}} = \frac{x \text{ cm}}{24 \text{ m}} \]

  2. Cross-multiply to solve for \( x \): \[ 4 \text{ cm} \times 24 \text{ m} = 3 \text{ m} \times x \text{ cm} \] \[ 96 = 3x \]

  3. Now, solve for \( x \): \[ x = \frac{96}{3} = 32 \]

Therefore, the length of the patio in the drawing is 32 centimeters.