Question

The side of an equilateral triangle expands at the rate of √3 cm/sec. When the side is 12 cm, the rate of increase of its area is .......,Select correct option from the given options.
(a) 12cm²/sec
(b) 18cm²/sec
(c) 3√3 cm²/sec
(d) 10cm²/sec

Answer 1

answer : option (b) 18 cm²/s

explanation : Area of equilateral triangle , A = √3/4 s² , where s is side length of equilateral triangle.

now differentiate , A = √3/4 s² with respect to time.

i.e., dA/dt = (√3/4) 2s ds/dt

⇒dA/dt = (√3/2)s ds/dt

given, The side of an equilateral triangle expands at the rate of √3 cm/sec.

i.e., ds/dt = √3 cm/s

and s = 12 cm

so, dA/dt = (√3/2) × 12 × √3

= 18 cm²/s