# 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.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

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, ha=4h2+42h.

### Explanation of Solution

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 ha cm.

Thus, by the Pythagoras theorem, h2=b2+42.

This implies, b=h2+42.

Area of the triangle is A=12×base×height.

Here, the base is hypotenuse h cm and the height is ha cm.

So, the area is, A=12×h×ha. (1)

If the base is 4 and the height is b, then the area is, A=12×4×b. (2)

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

12×h×ha=12×4×h2+42[b=h2+42]h×ha=4h2+42

The length of the altitude ha is to be expressed as a function of hypotenuse.

Therefore, ha=4h2+42h.

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