1.

The sides of an equilateral triangle are increasing at the rate of sqrt 3 cm/sec. find the rate at which the area of the triangle is increasing when the side is 4 cm long.

Answer»

Solution :Let x be the LENGTH of each SIDE of an equilateral TRIANGLE :
Given thatdx/dt =`SQRT 3` cm/sec. if A is the area of the triangle then
`A = sqrt 3/4 x^2 rArr dA/dt = sqrt 3/4 cdot 2x dx/dt = sqrt 3/2 x cdot dx/dt`
Now dA/dt](x=4) = sqrt 3/2 xx 4xx sqrt 3=6`
therefore Area of the triangle is INCREASING at the rate of 6 `cm^2/sec`.


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