Question

A triangle has side lengths 10 feet, 𝟤𝟢𝟧⎯⎯⎯⎯⎯⎯√square root of 205 feet, and 𝟣𝟢𝟧⎯⎯⎯⎯⎯⎯√square root of 105 feet. Is this a right triangle? Explain.

Answer 1

Yes. Square the side lengths: 10^2 = 100, (√205)^2 = 205, (√105)^2 = 105. The largest side is √205, and 205 = 100 + 105, so (√205)^2 = 10^2 + (√105)^2. By the converse of the Pythagorean theorem the triangle is right, with the right angle opposite the side √205.