Question

A child 4and a half feet tall casts a 6-foot shadow. A nearby statue casts an 18-foot shadow, creating a similar triangle to the child’s shadow as shown below. What is the height of the statue?

Answer 1

By using the concept of similar triangles, we find that the statue's height is 13.5 feet, based on the proportion between the child's height and shadow and the statue's shadow.

Step-by-step explanation:

To determine the height of the statue, we can use the concept of similar triangles, which states that corresponding sides of similar triangles are proportional. The child's height and shadow create one triangle, and the statue and its shadow create another similar triangle. We set up the proportion based on the relationship between the heights and the shadows.

Child's height (4.5 feet) / Child's shadow (6 feet) = Statue's height (unknown) / Statue's shadow (18 feet).

By cross-multiplying, we get:

4.5 feet × 18 feet = 6 feet × Statue's height

Statue's height = (4.5 feet × 18 feet) / 6 feet

Statue's height = 13.5 feet

Therefore, the height of the statue is 13.5 feet.