Answer:
2.114 cm.sec
Step-by-step explanation:
Given that an isosceles right triangle with legs of length s has area A.
At the instant when s 32 2 centimeters, the area of the triangle is increasing at rate of 12 square centimeters per second.
For a right triangle with legs = s each , area
= [tex]A= \frac{s^2}{2}[/tex]
Differentiate with respect to t
We get
[tex]\frac{dA}{dt}= \frac{1}{2}(2s) \frac{ds}{dt} \\ \frac{ds}{dt}= \frac{1}{s} \frac{dA}{dt}[/tex]
When dA/dt = 12 and A =32.2 we get
[tex]\frac{ds}{dt}= \frac{1}{s}* 12\\12*\sqrt{\frac{1}{2A} }\\= 1.49534[/tex]
Hypotenuse
[tex]h^2 = 2s^2\\h = \sqrt{2} s\\\frac{dh}{dt}=\sqrt{2} \frac{ds}{dt} \\=\sqrt{2}*1.49534\\=2.114[/tex]
