Question

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 9
feet long and Ariadne's shadow is 6
feet long. If Dixon is 6
feet tall, how tall is Ariadne?

Answer 1

To find Ariadne's height, we can use the concept of similar triangles. The ratio of the height of a person to the length of their shadow is the same for both Dixon and Ariadne.

Given:
- Dixon's height (H_D) = 6 feet
- Dixon's shadow (S_D) = 9 feet
- Ariadne's shadow (S_A) = 6 feet
- Ariadne's height (H_A) = ?

We can set up a proportion based on the heights and shadows:

\[
\frac{H_D}{S_D} = \frac{H_A}{S_A}
\]

Substituting the known values into the equation:

\[
\frac{6}{9} = \frac{H_A}{6}
\]

Now, cross-multiply to solve for \(H_A\):

\[
6 \cdot 6 = 9 \cdot H_A
\]
\[
36 = 9H_A
\]

Now, divide both sides by 9:

\[
H_A = \frac{36}{9} = 4
\]

Therefore, Ariadne is **4 feet tall**.