A triangle has two sides of length 8 cm and 10 cm. Select all the values of its third side that would make it a right triangle.
6 cm
18 cm
2 cm
√164 cm
√18 cm
What are possible values for the third side of a triangle with side lengths of 8 cm and 10 cm to make it a right triangle?
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To determine the possible lengths for the third side of a triangle that would make it a right triangle, we can use the Pythagorean theorem. For a triangle with sides ( a ), ( b ), and ( c ), where ( c ) is the longest side, the relationship is:
[ a^2 + b^2 = c^2 ]
Given two sides of lengths 8 cm and 10 cm, we will check which of the provided options can be the third side.
1. 6 cm:
– ( 8^2 + 6^2 = 64 + 36 = 100 )
– ( 10^2 = 100 )
– This is valid.
2. 18 cm:
– ( 10^2 + 8^2 = 64 + 100 )
– This would not hold since ( 10^2 + 8^2 = 164 neq 18^2 ).
– This is not valid.
3. 2 cm:
– ( 8^2 + 2^2 = 64 + 4 = 68 )
– ( 10^2 = 100 )
– This is not valid.
4. √164 cm:
– ( 8^2 + 10^2 = 64 + 100 = 164 )
– This