Question 628926
<pre>
We try the Pythagorean theorem which holds true 
for and only for right triangles:

      {{{(matrix(2,1,

Shortest, Side))^2}}} + {{{(matrix(2,1,

Medium, Side))^2}}} = {{{(matrix(2,1,

Longest, Side))^2}}} 

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A triangle with lengths 2, 3, 4

2² + 3² &#8799; 4²
  4 + 9 &#8799; 16
     13 &#8799; 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 &#8799; 10²
36 + 64 &#8799; 100
    100 &#8799; 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 &#8799; 13²
49 + 144 &#8799; 169
     193 &#8799; 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 &#8799; 17²
64 + 225 &#8799; 289
     289 &#8799; 289

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

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Edwin</pre>