8.7 求解图形相似应用题

在以下两个练习中，请使用所示地图。在地图上，圣安东尼奥、奥马哈和哥伦布三地构成一个三角形，其边长如图所示。圣安东尼奥到奥马哈的实际距离为 $802$ 英里。

ⓐ 求圣安东尼奥和哥伦布之间的实际距离。将答案四舍五入到小数点后一位。

[0.5] [0]

$1102.8 英里$

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.

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

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

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

Step 7 of 7

Answer the question.

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

ⓑ 求奥马哈和哥伦布之间的实际距离。将答案四舍五入到小数点后一位。

[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.

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

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

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

Step 7 of 7

Answer the question.

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

†