Propositiones ad Acuendos Juvenes/Problems/27 - De Civitate Quadrangula

by : Problem $27$

 * De Civitate Quadrangula: A Four-Sided Town
 * A four-sided town measures $1100$ feet on one side
 * and $1000$ feet on the other side;
 * on one edge $600$
 * and on the other edge $600$.


 * I want to cover it with roofs of houses,
 * each of which should be $40$ feet long
 * and $30$ feet wide.


 * How many dwellings can I make there?

Solution
The two long sides add up to $2100$ feet.

Similarly the two short sides add up to $1200$ feet.

Then the half of $1200$ is $600$, and the half of $2100$ is $1050$.

Because each house is $40$ feet long and $30$ feet wide:
 * take the $40$th part of $1050$ which is $26$
 * and the $30$th part of $600$ which is $20$.

$20$ times $26$ is $520$.

That is how many houses can be built.