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which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?
the triangle is a right triangle because 52 + 122 = 132
the triangle is a right triangle because 5 + 13 > 12.
the triangle is not a right triangle because 52 + 132 > 122
the triangle is not a right triangle because 5 + 12 > 13.
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5^2+12^2=13^2

Step-by-step explanation:

5^2+12^2=25+144=169

13^2=169

so 5^2+12^2=13^2

 The triangle is a right triangle because 5²+12²= 13²  .

Step-by-step explanation:

According to the converse of Pythagoras theorem , if the square of largest side of triangle is equal to the sum of squares of other two sides, then it is a right triangle.

The given side-lengths of triangle = 5 cm, 13 cm, and 12 cm

Here , 13²= 169

and 5²+12²=25+144=169

i.e.  the square of largest side of triangle is equal to the sum of squares of other two sides.

Thus , by converse of Pythagoras theorem, we can say that it is a right triangle.

Therefore  , the correct answer : The triangle is a right triangle because 5²+12²= 13²  .

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