Math Problem Statement

A classroom measures 12 meters long and 9 meters wide. When using a scale of 1 centimeters to 1.5 meters to draw the room on your paper, the size would be

Solution

To calculate the size of the classroom on paper using the given scale of 1 cm = 1.5 meters, follow these steps:

Step 1: Convert the actual dimensions to the scaled dimensions

  • Length of the room (12 meters):
    Scaled length=Actual lengthScale factor=121.5=8cm\text{Scaled length} = \frac{\text{Actual length}}{\text{Scale factor}} = \frac{12}{1.5} = 8 \, \text{cm}

  • Width of the room (9 meters):
    Scaled width=Actual widthScale factor=91.5=6cm\text{Scaled width} = \frac{\text{Actual width}}{\text{Scale factor}} = \frac{9}{1.5} = 6 \, \text{cm}

Step 2: State the dimensions on paper

The classroom would measure 8 cm by 6 cm on paper.

Final Answer:

The size of the classroom on paper is 8 cm × 6 cm.


Would you like a detailed explanation of the scale conversion process? 😊

Here are 5 related questions to expand your understanding:

  1. How do you calculate the area of the classroom on paper versus in real life?
  2. If the scale changed to 1 cm = 2 meters, what would the new dimensions be?
  3. How do scales work in map drawing or architectural designs?
  4. How would the size change if the classroom were measured in feet instead of meters?
  5. What would be the diagonal length of the scaled classroom drawing?

Tip: Always check the scale factor carefully when converting measurements to ensure accuracy in scaled drawings!

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Math Problem Analysis

Mathematical Concepts

Scale Conversion
Ratio and Proportion
Measurement

Formulas

Scaled Dimension = Actual Dimension / Scale Factor

Theorems

Basic principles of scaling in geometry

Suitable Grade Level

Grades 6-8