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?
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 9 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 6 feet. The height of the triangle is unknown.
Ariadne is blank feet tall.
The solution is
Ariadne's height can be found by setting up a proportion between Dixon's shadow and height and Ariadne's shadow and height.
Since Dixon's shadow is 9 feet long and Dixon's height is 6 feet, the proportion can be set up as follows:
9 feet (Dixon's shadow) / 6 feet (Dixon's height) = 6 feet (Ariadne's shadow) / x (Ariadne's height)
Simplifying the proportion, we get:
9/6 = 6/x
Cross-multiplying, we have:
9x = 6 * 6
9x = 36
Dividing both sides by 9, we get:
x = 36/9
x = 4
Therefore, Ariadne's height is 4 feet tall.