Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 15

Question

feet long and Ariadne's shadow is 6
feet long. If Dixon is
feet tall, how tall is Ariadne?

An image shows Dixon and Ariadne standing next to each other. Dixon forms a right triangle with a line going from the end of his shadow to the top of his head. The base of the triangle is 18 feet. The height of the triangle is 6 feet. Ariadne forms a right triangle with a line going from the end of her shadow to the top of her head. The base of the triangle is 15 feet. The height of the triangle is unknown.

Answer 1

To determine Ariadne's height based on the information given about their shadows and heights, we can use the concept of similar triangles.

We know that:

• The ratio of the height of an object to the length of its shadow is constant for both Dixon and Ariadne because they are standing in the same sunlight conditions.

Let's denote:

• \( D \) as Dixon's height (which we need to find out).
• \( A \) as Ariadne's height.
• \( S_D \) as Dixon's shadow length = 15 feet.
• \( S_A \) as Ariadne's shadow length = 6 feet.

From the problem, we have the following proportions based on their heights and shadow lengths:

\[ \frac{D}{S_D} = \frac{A}{S_A} \]

Substituting in the known values gives us:

\[ \frac{D}{15} = \frac{A}{6} \]

To find Ariadne's height (A), we can rearrange this equation:

\[ A = \frac{6}{15} \cdot D \]

Simplifying this gives:

\[ A = \frac{2}{5} \cdot D \]

Now, if we know how tall Dixon is (let's say he's \( D \) feet tall), we can plug in that value to find Ariadne's height.

For example, if Dixon is 5 feet tall:

\[ A = \frac{2}{5} \cdot 5 = 2 \text{ feet} \]

If you provide Dixon's height, I can calculate Ariadne's height for you.