Question

1. scenery the intersection of the two paths shown forms two similar triangles. if ac is 50 yards, mp is 35 yards, and the fountain is 5 yards from the intersection, about how far from the intersection is the stadium entrance? round to the nearest yard.

Explanation:

Step1: Set up the proportion

Since the two triangles are similar, the ratios of their corresponding sides are equal. Let the distance from the intersection to the stadium entrance be $x$. We have the proportion $\frac{MP}{AC}=\frac{5}{x}$.

Step2: Substitute the given values

Substitute $MP = 35$ yards and $AC=50$ yards into the proportion: $\frac{35}{50}=\frac{5}{x}$.

Step3: Cross - multiply

Cross - multiplying gives us $35x = 5\times50$.

Step4: Solve for $x$

$35x=250$, so $x=\frac{250}{35}=\frac{50}{7}\approx7$ yards.

Answer:

7 yards