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

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

• A. 10
• B. 5√3
• C. 5
• D. 5√2

Answer: (B)

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.