SOLUTION: Which of the following triangles could be right triangles? Check all that apply. A triangle with lengths 2, 3, 4 B. A triangle with lengths 6 inches, 8 inches, 10 inches

Algebra ->  Test -> SOLUTION: Which of the following triangles could be right triangles? Check all that apply. A triangle with lengths 2, 3, 4 B. A triangle with lengths 6 inches, 8 inches, 10 inches       Log On


   

Question 628926: Which of the following triangles could be right triangles? Check all that apply.
A triangle with lengths 2, 3, 4
B. A triangle with lengths 6 inches, 8 inches, 10 inches
C. A triangle with lengths 7, 12, 13
D. A triangle with lengths 8, 15, 17

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We try the Pythagorean theorem which holds true 
for and only for right triangles:

      %28matrix%282%2C1%2C%0D%0A%0D%0AShortest%2C+Side%29%29%5E2 + %28matrix%282%2C1%2C%0D%0A%0D%0AMedium%2C+Side%29%29%5E2 = %28matrix%282%2C1%2C%0D%0A%0D%0ALongest%2C+Side%29%29%5E2 

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A triangle with lengths 2, 3, 4

2² + 3² ≟ 4²
  4 + 9 ≟ 16
     13 ≟ 16

No, the Pythagorean theorem does not work, so a
triangle with sides 2,3,4 is not a right triangle.

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B. A triangle with lengths 6 inches, 8 inches, 10 inches 

6² + 8² ≟ 10²
36 + 64 ≟ 100
    100 ≟ 100

Yes, the Pythagorean theorem works, so a
triangle with sides 6,8,10 is a right triangle.

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C. A triangle with lengths 7, 12, 13 

7² + 12² ≟ 13²
49 + 144 ≟ 169
     193 ≟ 169

No, the Pythagorean theorem does not work, so a
triangle with sides 7,12,13 is not a right triangle.

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D. A triangle with lengths 8, 15, 17 

8² + 15² ≟ 17²
64 + 225 ≟ 289
     289 ≟ 289

Yes, the Pythagorean theorem works, so a
triangle with sides 8,15,17 is a right triangle.

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Edwin