Question : What is the altitude of an equilateral triangle whose side is 15 cm?
Option 1: $15\sqrt3\text{ cm}$
Option 2: $10\sqrt 3\text{ cm}$
Option 3: $\frac{9\sqrt 3 }{2}\text{ cm}$
Option 4: $\frac{15\sqrt 3}{2}\text{ cm}$
Correct Answer: $\frac{15\sqrt 3}{2}\text{ cm}$
Solution :
Given: The side of the triangle is 15 cm.
Let the altitude be $x$ cm.
The length of the altitude of an equilateral triangle = $\frac{\sqrt3}{2}$ × side of the triangle.
⇒ $x = \frac{\sqrt3}{2}\times15$
⇒ $x = \frac{15\sqrt3}{2}$
Hence, the correct answer is $\frac{15\sqrt3}{2}\text{ cm}$.
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