Exercise 1 Page 614

Let's take a look at the given picture. Notice that $∠ B C A$ and $∠ D C E$ are congruent as they are vertical angles.

Therefore, by the Angle-Angle Similarity Theorem, triangles

A C B

and

E C D

are similar. This means that corresponding sides of these triangles are proportional.

\frac{A B}{E D} = \frac{B C}{D C}

Now we will substitute the given side lengths and solve the proportion to find the length of

\overline{A B} .

\frac{A B}{E D} = \frac{B C}{D C}

Substitute values

\frac{A B}{1 0} = \frac{1 8}{2 2 . 5}

Cross multiply

A B \cdot 22.5 = 10 \cdot 18

$LHS / 22.5 = RHS / 22.5$

A B = \frac{1 0 \cdot 1 8}{2 2 . 5}

A B = \frac{1 8 0}{2 2 . 5}

Calculate quotient

A B = 8

The width of the ravine, which is congruent to

\overline{A B},

is

8

feet. This corresponds with answer D.