Question

A circular Park of radius 20 metre is situated in a Colony three boys Ankur Syed And Dravid are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other find the length of the string of each phone.

Answer 1

$\bf\huge\color{Navy}{Answer}$

$\underline{\underline{\bold{Question}}}$

A circular Park of radius 20 metre is situated in a Colony three boys Ankur Syed And Dravid are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other find the length of the string of each phone.

$\underline{\underline{\bold{Solution}}}$

$<b>Let find the circumference of the circular park .</b>$

Radius = 20m

Circumference = 2$\pi$r

= 2 × $\frac{22}{7}$ × 20m

= $\frac{880}{7}$m = 125.714m.

$\underline{\underline{\bold{Note}}}$

$<b> The three boys are sitting at equal distance. </b>$

length of the string = $\frac{125.714m}{3}$ = 41.90m

$\therefore$ the length of the string of each phone is 41.9m

Hope it helps you !!

Answer 2

Answers:

First, draw a diagram according to the given statements. The diagram will look as follows

Here the positions of Ankur, Syed and David 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

20 m = 2/3 × √3a/2

a = 20√3 m

So, the length of the string of the toy is 20√3 m.