A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is increasing by 4 in/sec and the long leg is
shrinking at 9 in/sec. What is the rate of change of the hypotenuse?

Given:

A right triangle has legs of 18 inches and 24 inches.

The short leg is increasing by 4 in/sec and the long leg is  shrinking at 9 in/sec.

To find:

The rate of change of the hypotenuse.

Solution:

Let x be the shorter leg (Base), y be the larger leg (Perpendicular) and z be the hypotenuse.

We have,

According to the Pythagoras theorem,

          ...(i)

Taking square root on both sides.

Side cannot be negative. So,

Differentiating (i) with respect to time t, we get

Divide both sides by 60.

Here, negative sign means hypotenuse is decreasing.

Therefore, the hypotenuse is shrinking at 4.8 in/sec.

the 3rd option is right

step-by-step explanation:

-2 is the right