   Chapter 1, Problem 2P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.

To determine

To express: The length of the hypotenuse as a function of the perimeter.

Explanation

Given:

The altitude perpendicular to the hypotenuse a=12 cm

Formula used:

Area of the triangleA=12(xy) (1)

Pythagoras theorem x2+y2=h2 (2)

Where, h is a hypotenuse, and x, y is the sides of triangle

Perimeter of the triangle P=x+y+h (3)

(x+y)2=x2+y2+2xy

Calculation:

Consider the triangle as shown below in the Figure 1.

From the Figure 1, A=12(ah)

Substitute a=12 in above equation,

A12(12h)=6h

From the equation (1),

A= 12(xy)

This implies xy=2A (4)

Consider the equation (x+y)2=x2+y2+2xy

Substitute the values of equation (1) and equation (2) in above equation,

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

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