Question

The map shows four towns connected by straight highways

Answer 1

We can solve this problem using the theorem that says that the altitude to the hypotenuse of a right triangle is the geometric mean between the segments into which the altitude divides the hypotenuse. Taking this into account, we can say that:

`(100)/(x)=(x)/(30)`

Solving for x, we have:

`100\cdot30=x\cdot x\Rightarrow x^2=3000`

Extracting the square root to both sides of the equation, we have:

`\sqrt[]{x^2}=\sqrt[]{3000}\Rightarrow x=54.7722557505`

To the nearest mile, we have x = 55 miles.