Question

Plz answer with explanation.

Answer 1

Answer:

(c) 3a√3/2

Step-by-step explanation:

Method 1:

Given:

Length of one side = 3a

Therefore, length of base = 3a [as it is an equilateral triangle]

Since it is an equilateral triangle and the perpendicular is drawn from a vertex, the perpendicular bisects the base.

Therefore, The distance between Vertex B and the point where the perpendicular meets the base is 3a/2

According to Pythagoras' theorem,

a² + b² = c²

So,

(3a/2)² + Altitude² = (3a)²

∴ 9a²/4 + Altitude² = 9a²

∴ Altitude² = 36a²/4 - 9a²/4

∴ Altitude² = 27a²/4

∴ Altitude = √27 * a/2

Also,

√27 * a/2

Ans = 3a√3/2

Method 2 [recommended]:

Area of an equilateral triangle = 1/2 * base * altitude

or

Area of an equilateral triangle = √3 * s * s/4

∴ √3 * s * s/4 = s * altitude/2             [base of an equilateral triangle = its side]

∴ √3 * s/2 = altitude

∴ altitude = 3a√3/2

Hope this helps! If it does feel free to mark it brainliest as it would really help. Thanks :D