Questions: On the blueprint of a house, 25 millimeters represents 4 meters. The actual length of the living room is 5 meters. What is its length on the blueprint? millimeters

Solution Steps

To find the length of the living room on the blueprint, we need to set up a proportion based on the given scale. The scale tells us that 25 millimeters on the blueprint corresponds to 4 meters in reality. We can use this ratio to find out how many millimeters correspond to 5 meters by setting up a proportion and solving for the unknown length on the blueprint.

We know from the problem that \( 25 \, \text{mm} \) on the blueprint represents \( 4 \, \text{m} \) in reality. We can express this relationship as a proportion: \[ \frac{25 \, \text{mm}}{4 \, \text{m}} = \frac{x \, \text{mm}}{5 \, \text{m}} \] where \( x \) is the length of the living room on the blueprint in millimeters.

To find \( x \), we can cross-multiply and solve the equation: \[ 25 \, \text{mm} \cdot 5 \, \text{m} = 4 \, \text{m} \cdot x \, \text{mm} \] This simplifies to: \[ 125 \, \text{mm} \cdot \text{m} = 4 \, \text{m} \cdot x \, \text{mm} \] Dividing both sides by \( 4 \, \text{m} \): \[ x = \frac{125 \, \text{mm} \cdot \text{m}}{4 \, \text{m}} = 31.25 \, \text{mm} \]

Final Answer