The two equal sides of an isosceles triangle with fixed base `b` are decreasing at the rate of `3c m//sdot` How fast is the area decreasing when the two equal sides are equal to the base?

Explanation

let base and equal sides of the triangle be a, b respectively

`AD= sqrt (a^2 - b^2/4)`

area `= 1/2*b* sqrt(a^2 - b^2/4)`

`(dA)/(dt) = 1/2*b1/sqrt(a^2 - b^2/4)*2a(da)/dt`

as `a=3 & da/dt= 3(cm)/s`

`(dA)/(dt) = 1/2*b*1/(2sqrt(3b^2/4))*2b*3`

`= (3b^2)/sqrt(3b^2)`

`= sqrt3 bcm^2`/s

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