# Two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/sec.How fast is the area decreasing when the two equal sides are equal to the base?

Jitender Singh IIT Delhi
8 years ago
Ans:
Let two equal sides of triangle to be ‘a’ at any instant (a is variable).
Area of triangle:
$A = \frac{1}{}2.b.\sqrt{a^{2}-\frac{b^{2}}{4}}$
$\frac{\partial A}{\partial x} = \frac{b}{2}.\frac{2a}{\sqrt{a^{2}-\frac{b^{2}}{4}}}.\frac{1}{2}.\frac{\partial a}{\partial x}$
$\frac{\partial a}{\partial x} = 3\frac{cm}{sec}$
$a = b$
$\frac{\partial A}{\partial x} = \frac{b}{2}.\frac{2b}{\sqrt{b^{2}-\frac{b^{2}}{4}}}.\frac{1}{2}.3 = \sqrt{3}b \frac{cm}{sec}$
Thanks & Regards
Jitender Singh
IIT Delhi