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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 7: Q35. (page 244)

Points Band C lies on $\overset{炉}{A D}$ . Find AC if $\frac{A B}{B D} = \frac{3}{4}, \frac{A C}{C D} = \frac{5}{6},$
and $B D = 66$ .

Short Answer

Expert verified

The length of AC is $52.5$ .

Step by step solution

01

Step 1. Given information.

$\frac{A B}{B D} = \frac{3}{4}, \frac{A C}{C D} = \frac{5}{6}$ and $B D = 66$

Point B and C lie on $\overset{炉}{A D}$ .

02

Step 2. Find the length of AB .

Substitute66 for BD in the equation $\frac{A B}{B D} = \frac{3}{4}$ .

$\begin{matrix} \frac{A B}{66} = \frac{3}{4} \\ A B = \frac{198}{4} \\ A B = 49.5 \end{matrix}$

03

Step 3. Find the length of the lineAB+BD .

$\begin{matrix} A B + B D = 49.5 + 66 \\ = 115.5 \end{matrix}$

From the length if AC and CD5x, let and6x be the measures.

The sum of AC and CD, is equal to the length of line.

$\begin{matrix} 5 x + 6 x = 115.5 \\ 11 x = 115.5 \\ x = 10.5 \end{matrix}$

04

Step 4. Now, find the length of AC .

Substitute $10.5$ for x in the 5x and 6x.

$\begin{matrix} A C = 5 x \\ = 5 脳 10.5 \\ = 52.5 \end{matrix}$

Therefore, the length of AC is $52.5$ .

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