8.7 닮은 도형의 활용 문제 풀기

다음 두 문제에서는 제시된 지도를 이용하세요. 지도 위에서 샌안토니오(San Antonio), 오마하(Omaha), 콜럼버스(Columbus) 는 아래 그림과 같이 세 변으로 이루어진 삼각형을 형성합니다. 샌안토니오에서 오마하까지의 실제 거리는 $802$ 마일입니다.

ⓐ 샌안토니오에서 콜럼버스까지의 실제 거리를 구하세요. 단, 소수점 아래 둘째 자리에서 반올림하여 소수 첫째 자리까지 나타내세요.

[0.5] [0]

$1102.8 마일$

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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