SajjadAhmad wrote:
If P is the perimeter of an equilateral triangle, which of the following represents the height of the triangle?
A. \(\frac{P}{3}\)
B. \(P\sqrt{3}/3\)
C. \(\frac{P}{4}\)
D. \(P \sqrt{3}/6\)
E. \(\frac{P}{6}\)
Since it is an equilateral triangle and its perimeter is P
then its side will be P/3. When we draw a height in an equilateral triangle the half portion of the triangle becomes 30-60-90 triangle. If we draw the height in it, the side opposite to 30 degree angle becomes P/6 since every side is P/3. To find the height we can use
Pythagoras Theorem.
Let the height be x,
The equation becomes, x^2 + (P/6)^2 = (P/3)^2
=> x^2 = (P/3)^2 - (P/6)^2
=> x^2 = P^2/9 - P^2/36
=> x^2 = (4P^2 - p^2) / 36
=> x^2 = 3P^2 /36
=> x^2 = P^2/12
=> x = P / √ 12
=> x = P * 2 √ 3 / 12
=> x= P √ 3 / 6
Answer is D
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Tashin