Mahender Singh stands on the tip of an equilateral triangle whose area is 36√3m^2. He goes around the three sides and return to the same tip. He goes to North end cover as much distance as before. He turns right and reach a point P which is parallel to the tip of the equilateral triangle. How far is he from the original point?
Answers
Given : Mahender Singh stands on the tip of an equilateral triangle whose area is 36√3m^2. He goes around the three sides and return to the same tip. He goes to North end cover as much distance as before. He turns right and reach a point P which is parallel to the tip of the equilateral triangle
To Find : How far is he from the Original point
Solution:
Area of Equilateral Triangle ABC ( A being vertex)
= (√3 / 4) Side² = 36√3
=> Side = 12 m
Hence perimeter = 36 m
covered 36 m .
AD ⊥ BC
=> AD = 6√3 m
From A goes in direction of DA to point P and AP = 36 m
then from P to Q
Now Δ APQ ~ Δ ADB
as ∠APQ = ∠ADB = 90° and ∠PAQ = ∠DAB ( vertically opposite angles)
=> AP / AD = AQ / AB
=> 36/ 6√3 = AQ/ 12
=> AQ = 72 /√3
=> AQ = 24√3 m
Hence he is 24√3 m far from initial point
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