   Chapter 4.4, Problem 44E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# In trap. ABCD, B C ¯ ⊥ A B ¯ and B C ¯ ⊥ C D ¯ . If D A = 17 ,       A B = 6           a n d           B C = 8 , find the perimeter of Δ D A C .

To determine

To Find:

The perimeter of ΔDAC.

Explanation

Consider the following trapezoid ABCD.

In a trapezoid ABCD, BC¯AB¯ and BC¯CD¯.

It is given that DA=17,AB=6andBC=8.

Consider the triangle ΔABC.

According to Pythagoras theorem, (AC)2=(AB)2+(BC)2.

Substitute, AB=6andBC=8.

Now, (AC)2=62+82=36+64=100.

Therefore, AC=10.

We know that, the diagonals of an isosceles trapezoid are congruent.

Then, BD=10.

Consider the triangle ΔBCD

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