The sides of an equilateral triangle are increasing at the 2cm per sec.Find the rate at which the area increases when the side is 10cm.
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Side of equilateral ∆ = 10cm.
Area of equilateral ∆ = √3 a^2 /4 sq.units.
Area of first ∆ = √3 10^2/4 sq. Cm.
= 25√3 sq. Cm.
Side increased by 2 cm. New side=12cm.
Area of second ∆ = √3 12^2 /4 sq. cm.
= 36√3 sq. Cm.
Increase in area
= 36√3 - 25√3=11√3sq.cm.per second
Rate of increase in area
(% in increase) = 11√3 x 100 / 25√3
= 44% per second
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