2. suppose that an isosceles right triangle is slowly expanding outwards with both legs of the triangle increasing at a rate of 10 cm/min. at the moment that the legs are 2 cm, how fast is the hypotenuse increasing in length? fully simplify your answer

=14.14 [cm/min]

Explanation:

If we have an isosceles right triangle we can use the Pythagoras theorem to find the hypotenuse:

(1)

(2)

From equation (2) let's take the derivative with respect to time (t):

dx/dt is the increasing rate of the triangle legs, it is dx/dt = 10 [cm/min].

=14.14 [cm/min] (3)

(3) is the hypotenuse increasing in length, and when x = 2 cm, using equation (2), h will be equal to 2.83 cm.

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