A tree is 56 feet tall and casts a 38 foot shadow. A person standing next to the tree is 5 feet tall. How long is their shadow? What does x equal and what is the proportion?
To find the length of the person's shadow, we can set up a proportion. Let's call the length of the person's shadow x.
The proportion can be set up as:
$\frac{56}{38} = \frac{5}{x}$
Cross multiplying, we get $56x = 38\cdot 5$, which simplifies to:
$56x = 190$
Dividing both sides by 56, we find:
$x = \frac{190}{56}$
Since this is not a simplified fraction, we can reduce it further. Dividing both the numerator and denominator by their greatest common factor of 2, we get:
$x = \frac{95}{28}$
So, the length of the person's shadow is $\frac{95}{28}$ feet, or approximately 3.39 feet.
The value of x is $\frac{95}{28}$, and the proportion is:
$\frac{56}{38} = \frac{5}{\frac{95}{28}}$