8.7 Solve Similar Figure Applications

In the following two exercises, use the map shown. On the map, San Antonio, Omaha and Columbus form a triangle whose sides are shown in the figure below. The actual distance from San Antonio to Omaha is $802$ miles.

ⓐ Find the actual distance from San Antonio to Columbus. Round your answer to the closest tenth.

[0.5] [0]

$1102.8 mi$

Step 1 of 7

ⓐ Read the problem. Draw the figures and label with the given information.

The figures are shown in the question.

Step 2 of 7

Identify what we are looking for: the actual distance from San Antonio to Columbus.

Step 3 of 7

Name the variables.

Let $x$ = distance from San Antonio to Columbus.

Step 4 of 7

Translate into an equation. Since the triangles are similar, the corresponding sides are proportional. We’ll make the numerators "miles" and the denominators "inches."

$\frac{x mi}{6.6 in} = \frac{802 mi}{4.8 in}$

Step 5 of 7

Solve the equation.

$\frac{x}{6.6} = \frac{802}{4.8}$

$x = 802 \cdot \frac{6.6}{4.8} = 1102.8 mi$

Step 6 of 7

Check.

Check $x = 1102.8 mi$ in the original proportion.

$\frac{x mi}{6.6 in} = \frac{802 mi2}{4.8 in}$

$\frac{1102.8 mi}{6.6 in}$ $\overset{?}{=}$ $\frac{802 mi}{4.8 in}$

$\frac{802 mi}{4.8 in}$ $\overset{?}{=}$ $\frac{802 mi}{4.8 in}$ ✓

Step 7 of 7

Answer the question.

The distance from San Antonio to Columbus is $1102.8$ miles.

ⓑ Find the actual distance from Omaha to Columbus. Round your answer to the closest tenth.

[0.5] [0]

$668.3 mi$

Step 1 of 7

ⓑ Read the problem. Draw the figures and label with the given information.

The figures are shown in the question.

Step 2 of 7

Identify what we are looking for: the actual distance from Omaha to Columbus.

Step 3 of 7

Name the variables.

Let $y$ = distance from Omaha to Columbus.

Step 4 of 7

Step 5 of 7

Solve the equation.

$\frac{y}{4} = \frac{802}{4.8}$

$y = 802 \cdot \frac{4}{4.8} = 668.3 mi$

Step 6 of 7

Check.

Check $y = 668.3 mi$ in the original proportion.

$\frac{y mi}{4 in} = \frac{802 mi2}{4.8 in}$

$\frac{668.3 mi}{4 in}$ $\overset{?}{=}$ $\frac{802 mi}{4.8 in}$

$\frac{802 mi}{4.8 in}$ $\overset{?}{=}$ $\frac{802 mi}{4.8 in}$ ✓

Step 7 of 7

Answer the question.

The distance from Omaha to Columbus is $668.3$ miles.

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