# One afternoon, Dave cast a 5-foot shadow. At the same time, his house cast a 20-foot shadow. If Dave is 5 feet 9 inches tall, how tall is his house?

Jun 12, 2016

His house is $23$ feet tall.

#### Explanation:

When Dave, whose shadow is $5$ feet, and that of his house, whose height is say $x$ feet, they in fact form, what is known as, similar triangles and shadows and respective heights of objects are proportional.

This is because shadows are formed by sun, who in comparison is at a huge distance. For example, if such shadows are formed by a beam of light from a lamp post, the same may not be in same proportion.

What this means is that Dave's height of $5$ feet $9$ inches i.e. $5 \frac{9}{12}$ or $5 \frac{3}{4} = \frac{23}{4}$ feet and his shadow of $5$ feet will be in same proportion as the ratio of height of the house at $x$ feet and its shadow of $20$ feet.

In other words, $\frac{\frac{23}{4}}{5} = \frac{x}{20}$ or

$\frac{23}{4 \times 5} = \frac{x}{20}$ or

$\frac{23}{20} = \frac{x}{20}$

or $x = 23$

Hence, his house is $23$ feet tall.