Question

6: cristobal is drawing a scale model of a giant redwood tree.

• the actual height of the tree is 12 meters.
• the scale of the model is \\(\frac{1}{6}\text{ cm} = \frac{1}{2}\text{ meter}\\).

what is the height, in centimeters, of the model tree?

Explanation:

🆕 New Concept Discovered: Scale Drawings and Models
Using ratios to relate model sizes to real-world sizes.

Step 1: Identify the given values and scale ratio

The actual height of the tree is \( 12 \) meters.

The scale is given as:

$$ \frac{1}{6}\text{ cm} = \frac{1}{2}\text{ meter} $$

This means that for every \( \frac{1}{2} \) meter of actual tree height, the model tree has a height of \( \frac{1}{6} \) centimeter.

Step 2: Set up a proportion

Let \( x \) be the height of the model tree in centimeters. We can set up a proportion comparing the model height to the actual height:

$$ \frac{\text{Model Height}}{\text{Actual Height}} = \frac{\frac{1}{6}\text{ cm}}{\frac{1}{2}\text{ m}} = \frac{x\text{ cm}}{12\text{ m}} $$

Step 3: Solve for the model height

To find \( x \), we can cross-multiply or multiply both sides of the equation by \( 12 \):

$$ x = 12 \cdot \frac{\frac{1}{6}}{\frac{1}{2}} $$

First, simplify the fraction on the right by multiplying by the reciprocal:

$$ \frac{\frac{1}{6}}{\frac{1}{2}} = \frac{1}{6} \cdot \frac{2}{1} = \frac{2}{6} = \frac{1}{3} $$

Now, multiply this scale factor by the actual height of \( 12 \) meters:

$$ x = 12 \cdot \frac{1}{3} $$

$$ x = 4 $$

Answer:

The height of the model tree is \( 4 \) centimeters.