Select whether the given side lengths of a triangle form a right triangle.
3 cm, 4 cm, 5 cm
8 m, 10 m, 15 m
6 in., 8 in., 10 in.
5 cm, 12 cm, 13 cm
Select whether the given side lengths of a triangle form a right triangle.
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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