Math Snap

STEP 1

1. The length of the soccer field in the drawing is $232$ millimeters.
2. The actual length of the soccer field is $116$ meters.
3. We need to determine the scale of the drawing in the form of $2$ millimeters to some number of meters.

STEP 2

1. Define the scale ratio.
2. Set up a proportion.
3. Solve the proportion for the scale.

STEP 3

Define the scale ratio as $\frac{2 \text{ mm}}{x \text{ meters}}$, where $x$ is the number of meters corresponding to $2$ millimeters in the drawing.

STEP 4

Set up a proportion based on the given lengths.
$$\frac{232 \text{ mm}}{116 \text{ meters}} = \frac{2 \text{ mm}}{x \text{ meters}}$$

STEP 5

Simplify the left side of the proportion.
$$\frac{232}{116} = 2$$ Thus, the proportion becomes:
$$2 = \frac{2 \text{ mm}}{x \text{ meters}}$$

Solve the proportion to find $x$.
Cross-multiply to solve for $x$:
$$2 \cdot x = 2 \cdot 1$$ Simplify:
$$2x = 2$$ Divide both sides by $2$:
$$x = 1$$ The scale of the drawing is:
$$2 \text{ millimeters} : 1 \text{ meter}$$