Drinks in dispute

As creator of riddles sometimes I receive emails asking me why such or which solution is given a prize when, according to their opinion, their solution was as good as the one that took it. It may speak of a mathematical problem in which the one who took the prize followed the habit of taking the result only to the third decimal, while the one who writes me complains that he was breaking his horns until he reached the tenth, giving clearly what he considers a better answer.

Keep in mind that I write since the nineteenth century and there are no calculators, so the good man has spent more than twelve pages to find his solution, while the winner approaches the solution by methods that anyone could understand and whose resolution does not occupy more than half page, but demonstrates having understood the principle of the riddle and that could take the answer to any number of decimals if an award was given to patience and endurance.

An referee cannot always respond to the reasons that lead him to give an award to one or the other, but the award -winning response will arrive several days before, or that it was clearer, or more intelligent and acute than the others. I tell you all these things to encourage you to be clear and concise when solving riddles. Move away from mathematical terms. The one that has to be clear is the solution, not explanations or arguments ..

In the illustration you can see some miners discussing their land. It seems that they had obtained permits on some farms of the same size. Each exploitation has the shape of a rectangle triangle, all with the same surface, but of different dimensions. A triangle has a 140 feet base, a height of 48 feet and a hypotenuse of 148, another has an 84 feet base, a height of 80 feet and a 116 -foot hypotenuse. Both triangles have an area of ​​3.360 feet.

¿What dimensions does the third triangle have, assuming that it has the same surface as the other two and that the three sides are whole?

Finding the third triangle with an area of ​​3360 feet, is so complicated that it is said that renowned mathematical such as Euler and Laplace said that it was impossible to discover a fourth triangle.

The dimensions are: Base 224 feet, height 30 feet, hypotenuse 226 feet.