Pythagoras theorem is applicable only in right angle triangle.
Area will be changing at the rate of (100/9) π cm²/sec.
Let us consider a right angle triangle have hypotenuse of 40 cm and acute angle is ∅.
So, Base is 40 cos ∅ and perpendicular is 40 sin ∅
Since, Area = 1/2 (base)(height)
A= 1/2 (40cos ∅)(40sin ∅)
A= 800sin ∅ cos ∅
A= 400 (2sin ∅ cos ∅)
A= 400sin 2∅
Differentiate above equation with respect to time.
dA/dt = 800 cos 2∅ (d∅/dt)
Since, d∅/dt is given π/36 rad/sec
So, dA/dt at ∅ = π/6
dA/dt = 800(1/2)(π/36)
dA/dt = (100/9)π cm²/sec.
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