Also be on the lookout for multiples like 10-24-26 and 2.5-6-6.5. The second Pythagorean triple that commonly appears on tests is 5-12-13 (5 2 + 12 2 = 13 2, 25 + 144 = 169).For example a right triangle with legs of length 6 and 8 will have a hypotenuse of 10 (6 2 + 8 2 = 10 2, 36 + 64 = 100). The ratio of a Pythagorean triple holds true even when the sides are multiplied by another number.When you see a right triangle with legs of length 3 and 4, you can instantly be certain that the hypotenuse will be 5 without having to do any calculations. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods. If you memorize the first 2 Pythagorean triples, in particular, you can save yourself a lot of time on these tests because you can immediately know the hypotenuse of one of these triangles just by looking at the side lengths! X Research source A 'side-based' right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. These special triangles appear frequently in geometry text books and on standardized tests like the SAT and the GRE. The side lengths of a Pythagorean triple are integers that fit the Pythagorean Theorem. Learn to recognize Pythagorean Triple Triangles.
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