   Chapter 4.4, Problem 48E 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 trapezoid ABCD, A B ¯ | | D C ¯ and m ∠ A = 90 ° . If A B = 7 ,       A D = 4           and           B C = 5 , Find the two possible lengths for side D C ¯ .

To determine

To find:

The length of the side DC¯.

Explanation

Consider the following trapezoid ABCD.

In a trapezoid ABCD, AB¯||DC¯ and mA=90°.

It is given that AB=7,AD=4 and BC=5.

Consider the triangle ΔABD.

According to Pythagoras theorem, (BD)2=(AB)2+(AD)2.

Substitute AB=7 and AD=4.

Then,

(BD)2=72+42=49+16=65

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