Question

1. outdoor sports in the figure, $\triangle abc \sim \triangle dbe$. how far is the archery range from the soccer field?
2. distances the triangles below are similar. what is the distance between tarryhill and tom’s falls?

Explanation:

Problem 4:

Step1: Set up similarity proportion

Since $\triangle ABC \sim \triangle DBE$, corresponding sides are proportional: $\frac{AC}{DE} = \frac{BC}{BE}$. Let $BC = x$ (distance between soccer field and archery range).
$\frac{24}{16} = \frac{x}{40}$

Step2: Solve for $x$

Cross-multiply: $16x = 24 \times 40$
$16x = 960$
$x = \frac{960}{16}$

Step1: Set up similarity proportion

The triangles are similar, so corresponding sides are proportional. Let $x$ = distance between Tarryhill and Tom's Falls.
$\frac{12}{48} = \frac{x}{84}$

Step2: Simplify and solve for $x$

Simplify $\frac{12}{48} = \frac{1}{4}$, so $\frac{1}{4} = \frac{x}{84}$
Cross-multiply: $4x = 84$
$x = \frac{84}{4}$

Answer:

60 yards

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Problem 6: