Chapter 4.4, Problem 40E

### 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

# Successive steps on a ladder form isosceles trapezoids with the sides. AH = 2 ft and BI = 2.125 ft.a) Find GN, the width of the bottom step.b) Which step is the median of the trapezoid with bases A H   ¯         a n d             G N ¯ ?

To determine

(a)

To Find:

GN

Explanation

Consider the following diagram.

It is given that successive steps of a ladder form an isosceles trapezoid.

Also given, AH=2ftâ€Šâ€Šâ€Šandâ€Šâ€ŠBI=2.125ft.

Now, BI becomes the median of the trapezoid AHCJ.

Then, BI=12(AH+CJ).

Substitute, AH=2ftâ€Šâ€Šâ€Šandâ€Šâ€ŠBI=2.125ft.

Therefore, 2.125=12(2+CJ).

Now, CJ=2â‹…2.125âˆ’2=2.25ft.

Similarly, CJ becomes the median of the trapezoid BIDK.

Then, CJ=12(BI+DK)

To determine

(b)

To Find:

The median of the trapezoid with the bases AH¯andGN¯.

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