Given the lengths of three sides of a triangle, which is a right triangle?

1. 10, 26, 24
2. 20, 12, 18
3. 30, 15, 26
4. 40, 50, 80

Also, explain why it is the answer.

Pythagorean Theorem: a 2 + b 2 = c 2 c represents the longest side of the triangle If the triangle is a right triangle, the Pythagorean theorem will be true.
(1) 10,24,26 1 0 2 + 2 4 2 = 676 2 6 2 = 676 1 0 2 + 2 4 2 = 2 6 2 Right Triangle
(2) 12,18,20 1 2 2 + 1 8 2 = 468 2 0 2 = 400 1 2 2 + 1 8 2  = 2 0 2 Not a right triangle
(3) 15,26,30 1 5 2 + 2 6 2 = 901 3 0 2 = 900 1 5 2 + 2 6 2  = 3 0 2 Not a right triangle
(4) 40,50,80 4 0 2 + 5 0 2 = 4100 8 0 2 = 6400 4 0 2 + 5 0 2  = 8 0 2 Not a right triangle
#1 is a right triangle

Answered by iloveonedirection | 2024-06-10

The only set of lengths that forms a right triangle is (1) 10, 26, 24, as it satisfies the Pythagorean theorem. The other sets do not meet the condition of the theorem. Therefore, the correct answer is option 1.
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Answered by iloveonedirection | 2024-12-24