Question

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. At what rate is the length of the hypotenuse of the triangle increasing in centimeters per second, at that instant?

Answer 1

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

= $A= \frac{s^2}{2}$

Differentiate with respect to t

We get

$\frac{dA}{dt}= \frac{1}{2}(2s) \frac{ds}{dt} \\ \frac{ds}{dt}= \frac{1}{s} \frac{dA}{dt}$

When dA/dt = 12 and A =32.2 we get

$\frac{ds}{dt}= \frac{1}{s}* 12\\12*\sqrt{\frac{1}{2A} }\\= 1.49534$

Hypotenuse

$h^2 = 2s^2\\h = \sqrt{2} s\\\frac{dh}{dt}=\sqrt{2} \frac{ds}{dt} \\=\sqrt{2}*1.49534\\=2.114$