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Q.

Let x be the length of one of the equal sides of an isosceles triangle  and let θ be the angle between them. If x is increasing at the rate of (1/12)m/hr and θ is increasing at the rate of π180 radians /hr, then  the rate in m2/hr at which the area of the triangle is increasing when x=12m and θ=π4

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a

2     12+π5

b

2

c

12+π5

d

π2

answer is A.

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Detailed Solution

ΔABC=12x2sin⁡θdΔdt=122xdxdtsin⁡θ+x2cos⁡θdθdt=xdxdtsin⁡θ+x22cos⁡θdθdt=(12)112×12+1442×12π180=12+π52
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