Question

A farmer has $5200 to spend on fencing to make a pen along a river. A local company tells the farmer that they can build the pen for $6.50/m. The manager suggests a pen in the shape of a right triangle with the hypotenuse along the river. What are the dimensions.

Answer 1

$5200 / $6.50/m = 800m of fence

maximum area for a given perimeter is a square, so we have an isosceles right triangle with both legs 400m long.