   Chapter 8.1, Problem 5E 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

In rhombus MNPQ, how does the length of the altitude from Q to P N ¯ compare to the length of the altitude from Q to M N ¯ ? Explain. Exercises 4–6

To determine

To Explain:

In rhombus MNPQ, the length of the altitude from Q to PN¯ and comparing it to the length of the altitude from Q to MN¯.

Explanation

Given,

In rhombus MNPQ,

The length of the altitude from Q to PN¯ is QR¯ and to the length of the altitude from Q to MN¯ is QS¯.

Find QR:

For the RPQ,

Here, PQ=x and RP=x2

By the Pythagorean theorem,

(RP)2+(QR)2=(PQ)2

(x2)2+(QR)2=(x)2

x24+(QR)2=(x)2

Add x24 on both sides,

x24+(QR)2x24=x2x24

(QR)2=4x2x24

(QR)2=3x24

QR=3x24

QR=32x

Fi

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