Chapter 4.4, Problem 46E

### 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

# In trapezoid 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, BCÂ¯âŠ¥ABÂ¯ and BCÂ¯âŠ¥CDÂ¯.

It is given that DA=17,â€Šâ€Šâ€ŠAB=6â€Šandâ€ŠBC=8.

Consider the triangle Î”ABC.

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

Substitute, AB=6â€Šandâ€ŠBC=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 Î”BCD

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