Question

Writing Exercises

428. Find a printed map and then write and solve an application problem similar to Example 8.79.

Answer 1

Given a map of San Francisco, Las Vegas and Los Angeles on which triangles are drawn.

We find that the distance from Los Angeles to San Francisco is 351 miles.

Explanation:

• Given a map of San Francisco, Las Vegas and Los Angeles on which triangles are drawn.

• We need to find the distance from Los Angeles to San Francisco.

• Since, the triangles are same and hence similar triangles, the corresponding sides are proportional.

• In the proportion, we will make numerators as miles and denominators as inches and solve the equation.

Step 1 of 2

In similar triangles, the corresponding sides are proportional.

We know that the distance between Los Angeles and Las Vegas is 270 miles and on the map it is 1 inches.

We need to form a proportion to find the distance between Los Angeles and San Francisco if on the map it is 1.3 inches.

Let the distance between Los Angeles and San Francisco be x .

`\begin{aligned}&\frac{\text { miles }}{\text { inches }}=\frac{\text { miles }}{\text { inches }} \\&\frac{x \text { Miles }}{1.3 \text { inches }}=\frac{270 \text { Miles }}{\text { linch }} \\&\text { Multiplying both sides by } 1.3 \text { we get, } \\&x=270 * 1.3 \text { Miles } \\&x=351 \text { Miles }\end{aligned}`

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

`\frac{x \text { Miles }}{\text { 1.3inches }}=\frac{270 \text { Miles }}{1 \text { inch }}$$`

We found x=351 Miles hence,

`$$\begin{aligned}&(351)/(1.3)=(270)/(1) \\&270=270 \\&\text { Here, } L H S=\text { RHS }\end{aligned}$$`

Hence, our answer is correct.