Question

In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks.

A map of the aquarium at the City Zoo. A triangle has points whales, sharks, dolphins. The distance from Whales to sharks is 54 feet and from whales to dolphins is 30 feet. A triangle with points Dolphins, fish tanks, penguins. The distance from dolphins to fish tanks is 45 feet, and from penguins to fish tanks is x feet.

What is the distance between the penguins and the fish tanks?
25 feet
36 feet
69 feet
81 feet

Answer 1

To find the distance between the penguins and the fish tanks (x), we can use the fact that the two triangles formed (Whales-Sharks-Dolphins and Dolphins-Fish Tanks-Penguins) are similar because their corresponding sides are parallel.

Given the following dimensions:
- Distance from Whales to Sharks = 54 feet (side of triangle 1)
- Distance from Whales to Dolphins = 30 feet (side of triangle 1)
- Distance from Dolphins to Fish Tanks = 45 feet (side of triangle 2)
- Distance from Penguins to Fish Tanks = x (side of triangle 2)

The triangles are similar, which gives us the proportion:
\[
\frac{Whales \, to \, Sharks}{Whales \, to \, Dolphins} = \frac{Dolphins \, to \, Fish \, Tanks}{Penguins \, to \, Fish \, Tanks}
\]

Substituting the known distances into the proportion:
\[
\frac{54}{30} = \frac{45}{x}
\]

Now we cross-multiply to solve for \( x \):
\[
54x = 30 \times 45
\]
\[
54x = 1350
\]
\[
x = \frac{1350}{54}
\]
\[
x = 25
\]

Thus, the distance between the penguins and the fish tanks is **25 feet**.