   Chapter 8.1, Problem 40E 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

Given: △ A B C , whose sides are 10 cm, 17 cm, and 21 cm. Find: a) BD, the length of the altitude to the 21-cm side b) The area of △ A B C , using the result from part (a) Exercises 39, 40

To determine

a)

To find:

The length of the altitude.

Explanation

Find the length of the altitude of the triangle is followed by the formula.

By Pythagorean theorem,

(BD)2+(DC)2=(BC)2

Calculation:

Given,

ABC, whose sides are 10 cm., 17 cm., and 21 cm., the length of the altitude BD to the 21-cm. side.

Let x be the length of DC and h be the length of the altitude BD.

For the right triangle BDC,

DC=x cm., BD=h cm., and BC=10 cm.

By Pythagorean theorem,

(BD)2+(DC)2=(BC)2

(h)2+(x)2=(10)2

h2+x2=100

Add (x2) on both sides,

h2+x2+(x2)=100+(x2)

h2+x2x2=100x2

h2=100x2

For the right triangle ADB,

AD=(21x) cm, BD=h cm, and AB=17 cm

To determine

b)

To find:

The area of ABC, using the result from part (a).

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