Question

Select all possible distances from bus b to bus a

Answer 1

Hello there. To solve this question, we'll have to remember some properties about the triangular inequality.

Given the following triangle in which the buses A, B and C are its vertex:

We know that Bus C is 8 miles away from bus B and bus C is 23 miles away from bus A.

We want to determine the possible distances between the buses A and B.

For this, remember the triangular inequality:

For any three sides of a triangle, say x, y and z, the biggest side z has to satisfy

`z\leq x+y`

So we're able to find an inequality that gives us the possible sides of the triangle, and, hence, the distances between the buses.

Plugging x = 8 and y = 23, we get

`\begin{gathered} z\leq8+23 \\ \\ \\ \end{gathered}`

Also, z has to be greater than or equal to 23, since it is the biggest side, therefore

`23\leq z\leq31`

So the possible values we can choose from the options are between 23 and 31.

These are the answers in this case: 23, 25, 27 and 30