Question

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.

Answer 1

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