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.

step-by-step explanation:

and 90% of people marry there 7th grade love. since u have read this, u will be told good news 2night. if u don't pass this on nine comments ur worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of ur life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love u

read more on -