   Chapter 5.4, 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

Find the length of the altitude to the 8-in side of a triangle whose sides are 4, 6, and8 in. long.(Hint: See Example 7.)

To determine

To Find:

Length of the altitude.

Explanation

Given Length of the altitude to the 8-in. side of a triangle whose sides are 4, 6, and 8 in. in length.

The figure can be as,

From the given data,

Length of the sides of the triangle is 4, 6, and 8 in.

From the figure,

AB = 4 in. and AC = 6 in. and BC = 8 in. and the altitude AD¯ to BC¯ that is AD¯BC¯.

Let the altitude be h, and BD = x and DC= 8-x.

Now ADB is right triangle then

From the Pythagorean Theorem,

x2+h2=42x2+h2=16 ...(1)

And from another right triangle ADC,

(8x)2+h2=626416x+x2+h2=36

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