Question

A 6 ft. tall baby giraffe standing next to an adult elephant casts a 15 ft. shadow. If the adult elephant casts a shadow that is 20 ft. long, then how tall is it?

a) 8 ft
b) 9 ft
c) 12 ft
d) 10 ft

Answer 1

By using the properties of similar triangles, the adult elephant's height is calculated to be 8 feet tall, which corresponds to option (a).

Step-by-step explanation:

To solve the problem of determining the height of the adult elephant, we will use similar triangles. The similar triangles here are the shapes formed by the giraffe and its shadow and by the elephant and its shadow. Since similar triangles have corresponding sides that are proportional, we can set up a proportion with the known values and solve for the unknown value, which is the height of the elephant.

The given information allows us to set up the following proportion based on the giraffe's and the elephant's shadows:
Giraffe's height / Giraffe's shadow = Elephant's height / Elephant's shadow

Substituting the known values in we get:

6 ft / 15 ft = Elephant's height / 20 ft

Cross-multiply to solve for the elephant's height:

6 ft x 20 ft = 15 ft x Elephant's height

120 ft = 15 ft x Elephant's height
Elephant's height = 120 ft / 15 ft
Elephant's height = 8 ft

Therefore, the adult elephant is 8 feet tall, which corresponds to option (a) 8 ft.