Algebra> Two equal sides of an isosceles triangle ...

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?

Manvendra Singh chahar , 10 Years ago

Grade Upto college level

1 Answers

Jitender Singh

Last Activity: 10 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

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Algebra> Two equal sides of an isosceles triangle ...

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?

Manvendra Singh chahar , 10 Years ago

Jitender Singh

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LIVE ONLINE CLASSES

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