Select whether the given side lengths of a triangle form a right triangle.

To determine whether the given side lengths form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides: ( c^2 = a^2 + b^2 ).

1. 3 cm, 4 cm, 5 cm:

( 5^2 = 25 ) and ( 3^2 + 4^2 = 9 + 16 = 25 )

*Forms a right triangle.*

2. 8 m, 10 m, 15 m:

( 15^2 = 225 ) and ( 8^2 + 10^2 = 64 + 100 = 164 )

*Does not form a right triangle.*

3. 6 in., 8 in., 10 in.:

( 10^2 = 100 ) and ( 6^2 + 8^2 = 36 + 64 = 100 )

*Forms a right triangle.*

4. 5 cm, 12 cm, 13 cm:

( 13^2 = 169 ) and ( 5^2 + 12^2 = 25 + 144 = 169 )

*Forms