Problemas
Each of the following sets of numbers represents the side lengths of a triangle.Using what you know about the Pythugereun Theorem determine whether each set of lengths could forma right triangle Arangles in archinctire Drag each set of numbers into "right triangles"or "non-right triangles: square breast square fairness 5.12,13 9,40,41 9,20,21 7,24,25 245 20,30,31
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To determine whether each set of lengths could form a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.Let's apply the Pythagorean Theorem to each set of lengths:1. 5, 12, 13 - Check if 13 is the hypotenuse: 13^2 = 169 - Check if 5^2 + 12^2 = 169: 5^2 = 25, 12^2 = 144, 25 + 144 = 169 - Since 169 = 169, this set of lengths forms a right triangle.2. 9, 40, 41 - Check if 41 is the hypotenuse: 41^2 = 1681 - Check if 9^2 + 40^2 = 1681: 9^2 = 81, 40^2 = 1600, 81 + 1600 = 1681 - Since 1681 = 1681, this set of lengths forms a right triangle.3. 9, 20, 21 - Check if 21 is the hypotenuse: 21^2 = 441 - Check if 9^2 + 20^2 = 441: 9^2 = 81, 20^2 = 400, 81 + 400 = 481 - Since 441 ≠ 481, this set of lengths does not form a right triangle.4. 7, 24, 25 - Check if 25 is the hypotenuse: 25^2 = 625 - Check if 7^2 + 24^2 = 625: 7^2 = 49, 24^2 = 576, 49 + 576 = 625 - Since 625 = 625, this set of lengths forms a right triangle.5. 20, 30, 31 - Check if 31 is the hypotenuse: 31^2 = 961 - Check if 20^2 + 30^2 = 961: 20^2 = 400, 30^2 = 900, 400 + 900 = 1300 - Since 961 ≠ 1300, this set of lengths does not form a right triangle.Based on the above calculations, we can categorize the sets of lengths as follows:Right triangles:- 5, 12, 13- 9, 40, 41- 7, 24, 25Non-right triangles:- 9, 20, 21- 20, 30, 31