Question

in the map below, the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants.
map of the city zoo
zebras
80 feet
monkeys
x feet
lions
132 feet
tigers
120 feet
elephants
what is the distance between the lions and the monkeys?
40 feet
88 feet
92 feet
198 feet

Explanation:

Step1: Identify Similar Triangles

Since the paths are parallel, the triangles formed (Zebras - Lions - Monkeys and Tigers - Lions - Elephants) are similar by the AA (Angle - Angle) similarity criterion (vertical angles at Lions and alternate interior angles due to parallel lines).

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{\text{Zebras to Monkeys (80 ft)}}{\text{Tigers to Elephants (120 ft)}} = \frac{\text{Lions to Monkeys (}x\text{ ft)}}{\text{Lions to Tigers (132 ft)}}$.

Step3: Solve for \( x \)

Substitute the known values: $\frac{80}{120} = \frac{x}{132}$. Cross - multiply: $120x = 80\times132$. Calculate $80\times132 = 10560$. Then, $x=\frac{10560}{120}=88$.

Answer:

88 feet (corresponding to the option "88 feet")