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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 1P

To determine

**To express:** The length of the altitude which is perpendicular to the hypotenuse as a function of the length of the hypotenuse if one of the legs of a right triangle is 4 cm.

Expert Solution

**Solution:**

The length of the altitude as function of the length of the hypotenuse is,

The length of the one leg of a right angle triangle is 4 cm and the other length of the other leg is *b* cm.

Let the length of the hypotenuse is *h* cm and the length of the altitude which is perpendicular to the hypotenuse is *h _{a}
* cm.

Thus, by the Pythagoras theorem,

This implies,

Area of the triangle is

Here, the base is hypotenuse *h* cm and the height is *h _{a}
* cm.

So, the area is,

If the base is 4 and the height is *b*, then the area is,

Compare the equations (1) and (2) and simplify,

The length of the altitude *h _{a}
* is to be expressed as a function of hypotenuse.

Therefore,