In an equilateral triangle with side 10, which is the altitude?

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Multiple Choice

In an equilateral triangle with side 10, which is the altitude?

Explanation:
In an equilateral triangle, the altitude from a vertex also serves as a median, so it lands at the midpoint of the opposite side. With side length 10, the base is split into two segments of length 5 each. The altitude, together with these two segments, forms a right triangle whose hypotenuse is 10 and one leg is 5. Using the Pythagorean theorem, the altitude is sqrt(10^2 − 5^2) = sqrt(100 − 25) = sqrt(75) = 5√3. So the altitude length is 5√3.

In an equilateral triangle, the altitude from a vertex also serves as a median, so it lands at the midpoint of the opposite side. With side length 10, the base is split into two segments of length 5 each. The altitude, together with these two segments, forms a right triangle whose hypotenuse is 10 and one leg is 5. Using the Pythagorean theorem, the altitude is sqrt(10^2 − 5^2) = sqrt(100 − 25) = sqrt(75) = 5√3. So the altitude length is 5√3.

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