Question

The area of an equilateral triangle of side'a! H
feet is increasing at the rate of
4 sq.ft./sec. The rate at which the perimeter
is increasing is
8v
1)
4)
a
moat and attains the speed
318
V3
213
3)
a
2
a​

Answer 1

$area \: = \frac{ \sqrt{3} }{4} {a}^{2}$

$\frac{d(area)}{dt} = 2 \times \frac{ \sqrt{3} }{4} \times a \times \: \frac{da}{dt} = 4$

$\frac{da}{dt} = \frac{8}{ \sqrt{3} a}$

now,

$perimeter(p) = 3a$

$\frac{dp}{dt} = 3 \times \frac{da}{dt} = 3 \times \frac{8}{ \sqrt{3} a} = \frac{8 \sqrt{3} }{a} ft \: per \: sec.$