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

Question

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.