Related rates problem another one

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the altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm^2.

do i use the pythagorin theorem for this
 
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I am seriously troubled by this. You are apparently in a calculus class but, honestly, you don't seem to have any idea of basic mathematics. Surely you know what the Pythagorean theorem IS: does this problem have anything to do with a right triangle? The problem specifically talks about the rate at which the area is changing and refers to the rates of change of base and altitude. What formula do you know for the area of a triangle?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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