Question

You enter a relay race. To start, you must run 20 yards to Checkpoint A. You then must turn and run 12 yards to Checkpoint B. Last, you must turn and run back to the starting line. What is the distance from Checkpoint B to the starting line? THANKS :)

Answer 1

The shortest distance between checkpoint A and checkpoint B is 23.33 yards.

Explanation:

We are given the following information in the question:

Let O be the starting point.

Distance between the starting point and checkpoint A = 20 yards

To reach checkpoint B, one need to take a turn and let it be a 90 degrees turn toward right or left.

Distance between checkpoint A and checkpoint B = 12 yards

In order to find the shortest distance between the checkpoint A and checkpoint B, the displacement, we use the Pythagoras theorem.

Statement:

In a right angled triangle:

`(Side 1)^2 + (Side 2)^2 = (Hypotenuse)^2`

`(OA)^2 + (AB)^2 = (AB)^2\\(20)^2 + (12)^2 = (AB)^2\\400 + 144 = (AB)^2\\(AB)^2 = 544\\AB = √(544) \approx 23.33`

Hence, the shortest distance between checkpoint A and checkpoint B is 23.33 yards.

Answer 2

Distance to checkpoint A from starting line = 20 yards.

Then from A to B distance = 12 yards.

Let us take starting point C.

So, it would make a right triangle.

We have AB = 12, AC = 20, we need to find BC, that is Hypotenuse of the right triangle.

According to Pythagoras theorem:

`BC^2 = AB^2+AC^2`

`BC^2 = 12^2+20^2`

`BC^2 = 144 +400 = 544`

`BC= √(544)`

BC = 23.32.

Therefore, 23.32 yards is the distance from Checkpoint B to the starting line.