Chapter 7: Q35. (page 244)

Points Band C lies on $\bar{A D}$ . 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

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 $\bar{A D}$ .

Step 2. Find the length of AB .

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

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

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.

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

Step 4. Now, find the length of AC .

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

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

Therefore, the length of AC is $52.5$ .

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Points Band C lies on $\bar{A D}$ . 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

Step by step solution

Step 1. Given information.

Step 2. Find the length of AB .

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

Step 4. Now, find the length of AC .

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Points Band C lies on AD¯. Find AC ifABBD=34,ACCD=56,andBD=66 .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the length of AB .

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

Step 4. Now, find the length of AC .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Probability and Statistics

Decision Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

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