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Determine if the triangles with the side lengths below are right triangles or not.

7, 20, 25 is not a right triangle

26, 24, 10 is a right triangle

13, 8, square root of 10 is not a right triangle

52, 48, 20 is a right triangle

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Option A; No,

Option B; Yes,

Option C; No,

Option D; Yes

Step-by-step explanation:

If these are right triangles, Pythagorean Theorem can be applied to them such that the smaller lengths are to be the legs, the larger of the two the hypotenuse;

Case 1; We are given a triangle with lengths 7, 20, and 25. Clearly the two legs must be those with lengths 7 and 20, the hypotenuse with length 25 units,

7^2 + 20^2 = 25^2,

49 + 400 = 625,

449 ≠ 625 ⇒ Thus these lengths do not form a right triangle

Case 2; We are given lengths 26, 24 , and 10 ⇒ where the legs are lengths 10 and 24, the hypotenuse of length 26,

10^2 + 24^2 = 26^2,

100 + 576 = 676,

676 = 676 ⇒ Thus these lengths do form a right triangle

Case 3; This triangle has legs of lengths 8 and √10, with a hypotenuse of length 13,

√10^2 + 8^2 = 13^2,

10 + 64 = 169,

74 ≠ 169 ⇒ Thus these lengths do not form a right triangle

Case 4; This triangle has legs of lengths 48 and 20, with a hypotenuse of length 52,

20^2 + 48^2 = 52^2,

400 + 2304 = 2704,

2704 = 2704 ⇒ Thus these lengths do form a right triangle

32

step-by-step explanation: