This math skill involves using Pythagorean triples to determine missing lengths in right triangles. Pythagorean triples are sets of three integers that satisfy the Pythagorean theorem. Commonly known triples, like (3, 4, 5), can be multiplied by any whole number to generate new triples. These triples can help identify similar triangles and solve for unknown sides.
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Pythagorean triples to solve triangle lengths
Test your understanding of Pythagorean triples to solve triangles by practicing it! Work through the below exercises to use it in practice.
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Use Pythagorean triples to solve the missing length on the larger triangle
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Pythagorean triples are integer solutions to the Pythagorean equation. 3, 4, and 5 is the most common one, but 5, 12, and 13 would be another.
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For any Pythagorean triple, you can also multiply the numbers by a whole number to create another Pythagorean triple. We can see that 6, 8, and 10 shares two numbers with our triangle.
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Since it has a shared right angle and two shared sides, it's a similar triangle, so the missing hypotenuse must be 10