Respuesta :
Answer:
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.
Step-by-step 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 .
[tex]\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 \times 1.3 \text { Miles } \\&x=351 \text { Miles }\end{aligned}[/tex]
Step 2 of 2
To check if the answer is reasonable, we substitute it back in the formed proportion
[tex]\frac{x \text { Miles }}{\text { 1.3inches }}=\frac{270 \text { Miles }}{1 \text { inch }}$[/tex]
We found x=351 Miles hence,
[tex]$\begin{aligned}&\frac{351}{1.3}=\frac{270}{1} \\&270=270 \\&\text { Here, } L H S=\text { RHS }\end{aligned}$[/tex]
Hence, our answer is correct.
