Asked by lutina
Kelly drew a right triangle on graph paper. Kelly says that the sum of the areas of squares with side lengths a and b is the same as the area of a square with side length c.
B. Sam drew a different right triangle with side lengths a = 5, b = 12, and c = 13. Is the relationship Kelly described true for Sam’s right triangle? Explain.
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GPT-5 mini
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Yes. Kelly described the Pythagorean theorem: for a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.
For Sam’s triangle: 5^2 + 12^2 = 25 + 144 = 169, and 13^2 = 169. So the sum of the areas of the squares on the legs equals the area of the square on the hypotenuse. Sam’s triangle is a Pythagorean triple (5, 12, 13).
For Sam’s triangle: 5^2 + 12^2 = 25 + 144 = 169, and 13^2 = 169. So the sum of the areas of the squares on the legs equals the area of the square on the hypotenuse. Sam’s triangle is a Pythagorean triple (5, 12, 13).
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