A word problem:
Bob wants to make a triangular yard. He knows that is is a right triangle and one degrees is 90 degrees. One leg is 3 yards and the other is 4 yards. What is the longest side?
So you use the theorem. This is an easy exmple.
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There are many limitations that mathematical models have as problem solving tools. There is always a margin of error for example.
in this problem solving in a rectangle width is 3 and the perimeter is 16 what is he length
When solving a math problem
well, i think the answer to your question is getting the measurement of the side using the Pythagorean Thereom, with the formula:c2=a2+b2.
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few