Mahender Singh stands on one edge of an equilateral triangle whose area is 36√3m^2. He goes around the three sides of the equilateral triangle and return to the same edge.Then he goes to North end cover as much distance as before. He turns right and reach a point P which is parallel to the edge of the equilateral triangle. How far is he from the initial point(edge)?
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Answers
Given : Mahender Singh stands on one edge of an equilateral triangle whose area is 36√3m^2. He goes around the three sides of the equilateral triangle and return to the same edge.
Then he goes to North end cover as much distance as before.
He turns right and reach a point P which is parallel to the edge of the equilateral triangle.
To Find : How far is he from the initial point(edge)
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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