We have to find which of the following could represent the lengths of the sides of a right triangle.
To be a right triangle, the lengths a, b and c have to satisfy the Pithagorean theorem:
[tex]a^2+b^2=c^2[/tex]Of course, c has to be the largest of the sides.
We can write for the first option:
[tex]\begin{gathered} 3^2+4^2=5^2 \\ 9+16=25 \\ 25=25 \end{gathered}[/tex]As the expression is satisfied, we can conclude that the triangles with sides 3, 4 and 5 is a right triangle.
Option B (5,12,12) can not be a right triangle, as it has 2 largest sides. It can only have one, that is the hypothenuse. NOTE: it can have two equal smallest sides, but no two largest.
Option C is 15, 30 and 45. We test the equation:
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