Chapter 5.4, Problem 31E

### 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

# Find the length of the altitude to the 26-in. side of a triangle whose sides are 10, 24, and 26 in. in length.

To determine

To Find:

Length of the altitude.

Explanation

Given Length of the altitude to the 26-in. side of a triangle whose sides are 10, 24, and 26 in. in length.

The figure can be as,

From the given data,

Length of the sides of the triangle is 10, 24, and 26 in.

From the figure,

AB = 10 in. and AC = 24 in. and BC = 26 in. and the altitude ADÂ¯ to BCÂ¯ that is ADÂ¯âŠ¥BCÂ¯.

Let the altitude be h, and BD = x and DC= 26-x.

Now ADB is right triangle then

From the Pythagorean Theorem,

x2+h2=102x2+h2=100Â Â ...(1)

And from another right triangle ADC,

(26âˆ’x)2+h2=242676âˆ’52x+x2+h2=576Â Â

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