   Chapter 8.1, Problem 47E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 47 to 50, use the fact that the area of the polygon is unique.In the right triangle, find the length of the altitude drawn to the hypotenuse. To determine

To find:

The length of the altitude drawn to the hypotenuse.

Explanation

Converting theoretical statement into mathematical statement, identifying the geometric figure and the calculation is done by suitable geometric formulae.

Calculation:

Given,

The lengths of the sides are,

AB=a=5 in

BC=b=12 in

Area of the right ΔABC(A)=12ab unit2.

=12(5)(12)

=(5)(6)

A=30 in2

Find AC:

For right triangle ABC

Here AB=5 in and BC=12 in

By Pythagorean theorem,

(AB)2+(BC)2=(AC)2

(5)2+(12)2=(AC)2

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