For a triangle with sides 8, 10, 6, what is the semiperimeter used in Heron's formula?

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Multiple Choice

For a triangle with sides 8, 10, 6, what is the semiperimeter used in Heron's formula?

Explanation:
In Heron's formula, s is the semiperimeter, which is half of the triangle’s perimeter. Add the sides: 8 + 10 + 6 = 24. Half of that is 24 ÷ 2 = 12, so the semiperimeter is 12. This value is used inside the square root in the formula, as in sqrt[s(s−a)(s−b)(s−c)]. For these sides, that would be sqrt(12·4·2·6) = sqrt(576) = 24, confirming the calculation is consistent.

In Heron's formula, s is the semiperimeter, which is half of the triangle’s perimeter. Add the sides: 8 + 10 + 6 = 24. Half of that is 24 ÷ 2 = 12, so the semiperimeter is 12. This value is used inside the square root in the formula, as in sqrt[s(s−a)(s−b)(s−c)]. For these sides, that would be sqrt(12·4·2·6) = sqrt(576) = 24, confirming the calculation is consistent.

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