Chapter 8.1, Problem 39E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# Given: △ A B C , whose sides are 13 in., 14 in., and 15 in. Find: a) BD, the length of the altitude to the 14-in. side(HINT: USE the Pythagorean Theorem twice.)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,

â–³ABC, whose sides are 13 in., 14 in., and 15 in., the length of the altitude BD to the 14-in. side.

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

For the right triangle â–³BDC,

DC=xÂ in.,Â BD=hÂ in., and BC=15Â in.

By Pythagorean theorem,

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

(h)2+(x)2=(15)2

h2+x2=225

h2+x2+(âˆ’x2)=225+(âˆ’x2)

h2+x2âˆ’x2=225âˆ’x2

h2+0=225âˆ’x2

h2=225âˆ’x2

To determine

b)

To find:

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

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