   Chapter 5.5, Problem 22E 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

Given: Rhombus A B C D (not shown) in whichdiagonals A C ¯ and D B ¯ intersect at point E ; D B = A B = 8 Find: A C

To determine

To find:

AC of a rhombus ABCD in which the diagonals AC¯ and BD¯ intersect at the point E with BD=AB=8

Explanation

Approach:

For a right triangle, for which the measure of the interior angles 30°, 60°, and 90°; if ‘a’ is the length of measure of the shorter leg; opposite to the angle 30°, then the length of the other two sides is given by

Length of the longer leg (opposite to 60°) =a3

Length of the hypotenuse (opposite to 90°)=2a.

In general

Length of the longer leg =3× (Length of the shorter leg)

Length of the hypotenuse =2× (Length of the shorter leg)

Calculation:

Given,

A rhombus ABCD with AC¯ and BD¯ as diagonals wjhich intersect at the point E, with BD=AB=8

By the property of a rhombus that all the four sides of a rhombus are congruent with that the diagonals are their perpendicular bisector we have,

AB¯BC¯CD¯DA¯,

AE¯EC¯; BE¯ED¯ and

AC¯BD¯

Thus,

AB=BC=CD=DA=8 units.

BE=DE=4 units

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 