Question

. In a circular park of radius 25 m, three girls Neha, Preeti and Reshma are sitting at equal

distance on its boundary each having a cellphone and talking to each other. Find the

distance between Neha and Reshma. (Take v3 = 1.732)​

Answer 1

Answer:

43.30m

Step-by-step explanation:

Here the positions of Neha, Preeti and Reshma are represented as A, B and C respectively. Since they are sitting at equal distances, the triangle ABC will form an equilateral triangle.

AD ⊥ BC is drawn. Now, AD is median of ΔABC and it passes through the centre O.

Also, O is the centroid of the ΔABC. OA is the radius of the triangle.

OA = 2/3 AD

Let the side of a triangle a metres then BD = a/2 m.

Applying Pythagoras theorem in ΔABD,

AB2 = BD2+AD2

⇒ AD2 = AB2 -BD2

⇒ AD2 = a2 -(a/2)2

⇒ AD2 = 3a2/4

⇒ AD = √3a/2

OA = 2/3 AD

25m = 2/3 × √3a/2

a = 25√3 m

So, the distance between Neha and Reshma is 25√3 m = 43.30m