In the diagram, points A and B are the positions of the cars. We are asked to find the distance between the cars. Let's start by taking a closer look at the diagram.
Note that segment AB consists of two segments. Each of the two segments is the hypotenuse of a right triangle. Therefore, to find the length of segment AB, we need to use the Pythagorean Theorem.
a^2+ b^2= c^2
In the formula, a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle. Let's start by finding the length of the hypotenuse of the smaller triangle. In this case, a= 6 and b= 8.
Let's substitute these values into the formula.
a^2+ b^2= c^2
⇕
6^2+ 8^2= c^2
Now we can solve an equation that we got to find the value of c.
Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, we got that the hypotenuse of the smaller triangle is 10 miles long. Next, we will find the length of the hypotenuse of the larger triangle. This time, a= 9 and b= 12.
Let's substitute these values into the formula.
a^2+ b^2= c^2
⇕
9^2+ 12^2= c^2
Now we can solve an equation that we got to find the value of c.
Again, a negative side length does not make sense, so we only need to consider positive solutions. Therefore, the hypotenuse of the larger triangle is 15 miles long. Finally, we can find the length of segment AB by adding the lengths of the hypotenuses.
10 + 15=25
We got that the length of segment AB is 25 miles. This means that the distance between the cars is 25 miles and D is the correct option.
