Solution: Yes, because 27, 36, and 45 are derived by multiplying each of 3, 4, and 5, which are Pythagorean triples, by 9. Sample Problem: Is 27, 36, and 45 a Pythagorean triple? If we multiply these three numbers by 4, we have 20, 48, and 52 these new triples are also Pythagorean triples. If you take the multiples of the triples listed above, you will still obtain a Pythagorean triple.įor instance, 5, 12, and 13 is a Pythagorean triple. You can try it and confirm that these triples are all Pythagorean triples. Some common Pythagorean triples are the following: Are these numbers Pythagorean triples?ġ, 2, and 3 failed to satisfy the Pythagorean theorem, so they are not triples. Notice how they satisfy the Pythagorean theorem:īoth sides are equal therefore, 3, 4, and 5 are Pythagorean triples. The smallest Pythagorean triples are 3, 4, and 5. Pythagorean triples are three positive whole numbers that satisfy the Pythagorean theorem. And since Q represents the measurement of a leg of the right triangle, the value of Q must be 8 cm. Therefore, the missing measurement of the leg of the right triangle is 8 cm long. Q 2 = -36 + 100 Transposition method (we isolate b from the constants) (6) 2 + (Q) 2 = (10) 2 One of the legs is 6 cm while the hypotenuse is 10 cm To find the missing measurement of a leg of a right triangle, we can use the Pythagorean theorem and manipulate the equation we will form.Ī 2 + b 2 = c 2 where a and b are the legs and c is the hypotenuse The other leg of the right triangle measures 6 cm, while its hypotenuse is 10 cm. Solution: In the figure above, Q represents the measurement of a leg. Sample Problem 3: What is the measurement of the side AB in the right triangle below? Therefore, we conclude that the shortest path from Helen’s house to the library is 50 meters long (try computing the total distance of all possible paths from Helen’s house to the library, and you will discover that the shortest distance is indeed the one represented by the diagonal line). It means that the diagonal line we draw measures 50 m. Thus, the hypotenuse of the right triangle we formed is 50. We let c as the length of the hypotenuse of the right triangle. The legs have measurements of 30 m and 40 m. The diagonal line will serve as the hypotenuse of this right triangle. We have already defined the legs of this triangle in the previous paragraph. Since we have formed a right triangle, we can apply the Pythagorean theorem to find the length of this diagonal line. The legs are the road from Helen’s house to the Acacia tree and the road from the Acacia tree to the library.Īnd what is the hypotenuse? None other than the diagonal line representing the shortest path from Helen’s house to the library. Notice that we have created a right triangle as we draw this diagonal line between Helen’s house and the library. The length of the diagonal line that we draw is the distance of the shortest path from Helen’s house to the library.
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