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 18 feet long and Ariadne's shadow is 15 feet long. If Dixon is 6 feet tall, how tall is Ariadne?

18 / 15 = 6 / x

multiply both sides by 15 x (or "cross multiply")

18 x = 15 * 6

x = 15 * 6/18 = 15/3 = 5 feet

To determine Ariadne's height, we can set up a proportion between the lengths of their shadows and their heights.

Let's represent Dixon's height as "D" and Ariadne's height as "A".

The proportion can be set up as:

Dixon's shadow length / Dixon's height = Ariadne's shadow length / Ariadne's height

Substituting the given values:

18 feet / 6 feet = 15 feet / A

To solve for Ariadne's height (A), we can cross-multiply:

18 feet * A = 15 feet * 6 feet

18A = 90 feet

Dividing both sides of the equation by 18:

A = 90 feet / 18

A = 5 feet

Therefore, Ariadne is 5 feet tall.

To determine Ariadne's height, we can use the concept of proportions and ratios in similar triangles.

First, we know that Dixon's shadow is 18 feet long and he is 6 feet tall. So, the ratio of the length of Dixon's shadow to his height is 18:6, which simplifies to 3:1.

Since Ariadne's shadow is 15 feet long, we can use the same ratio 3:1 to find her height. By multiplying the length of Ariadne's shadow (15 feet) by the ratio 1/3, we can determine her height.

15 feet * (1/3) = 5 feet

Therefore, Ariadne is 5 feet tall.

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