Question

6. A circular park of radius 20m is Situated in a colony. Three boys Ankur. Syed and
David 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

Answer:

x = 20 3m

Step-by-step explanation:

Let Ankur be represented as A, Syed as S and David as D.

he boys are sitting at an equal distance.

Hence, △ASD is an equilateral triangle.

Let the radius of the circular park be r meters.

∴OS=r=20m.

Let the length of each side of △ASD be x meters.

Draw AB⊥SD

∴SB = BD = 1/2 SD = x/2m

In △ABS, ∠B = 90 degree

By Pythagoras theorem,

AS^2 = AB^2 + BS^2

∴ AB^2 = AS^2 - BS^2 = x^2 - x/2^2 = 3x^2 / 4

∴AB = 3x / 2m

Now, AB = AO + OB

OB = AB − AO

OB = (3x / 2 - 20)m

In △OBS,

OS^2 = OB^2 + SB^2

20^2 = (3x / 2 - 20)^2 + x / 2^2

400 = 3/4x^2 + 400 - 2(20) (3x / 2) + x^2 / 4

0 = x^2 - 20 3x

x = 20 3m

Please mark me as the brainliest

Answer 2

Answer:

x=20 3 it's correct answer I guess