   Chapter 5.4, Problem 30E 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 10-in. side of a triangle whose sides are 6, 8, and 10 in. in length.

To determine

To Find:

Length of the altitude.

Explanation

Given Length of the altitude to the 10-in. side of a triangle whose sides are 6, 8, and 10 in. in length.

The figure can be as,

From the given data,

Length of the sides of the triangle is 6, 8, and 10 in.

From the figure,

AB = 6 in. and AC = 8 in. and BC = 10 in. and the altitude AD¯ to BC¯ that is AD¯BC¯.

Let the altitude be h, and BD = x and DC= 10-x.

Now ADB is right triangle then

From the Pythagorean Theorem,

x2+h2=62x2+h2=36  ...(1)

And from another right triangle ADC,

(10x)2+h2=82(10x)2+h2=64(10020x+x2)+h2=64

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