   Chapter 5.6, Problem 12E 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: D E ↔ ∥ B C , ¯ A D = 5 , D B = a + 3 , A E = a + 1 , E C = 3 ( a − 1 ) Find: a  and  E C To determine

To find:

a,EC.

Explanation

Given:

Theorem used:

If a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.

Calculation:

Given: DEBC¯

Since if a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.

Also given that AD=5,DB=a+3,AE=a+1,EC=3(a1).

Thus 5a+3=a+13(a1).

Now let us find the value of a.

5a+3=a+13(a1)15(a1)=(a+1)(a+3)15

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