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Chapter 5.6, Problem 7E
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### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Given: l 1 ∥ l 2 ∥ l 3 , A B = 4 , B C = 5 , D E = x , E F = 12 − x Find: x , D E , E F

To determine

To find:

x,DE,EF.

Explanation

Given:

l1âˆ¥l2âˆ¥l3 and AB=4,BC=5,DE=x,EF=12âˆ’x.

Theorem used:

When three (or more) parallel lines are cut by a pair of transversals, the transversals are divided proportionally by the parallel lines.

Calculation:

Given: l1âˆ¥l2âˆ¥l3

Since when three (or more) parallel lines are cut by a pair of transversals, the transversals are divided proportionally by the parallel lines.

â‡’ABDE=BCEF

Also given that AB=4,BC=5,DE=x,EF=12âˆ’x.

Thus 4x=512âˆ’x.

Now let us find the value of x.

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