SOLUTION: MY SON AND I HAVE BEEN TRYING TO FIGURE THIS EXPRESSION OUT FOR A WEEK NOW. I HOPE YOU CAN HELP. HERE IS THE SCENARIO: ONE DAY YOU DECIDE TO RELEASE YOUR PET HOMING PIGEONS IN

Question 34608: MY SON AND I HAVE BEEN TRYING TO FIGURE THIS EXPRESSION OUT FOR A WEEK NOW. I HOPE YOU CAN HELP.
HERE IS THE SCENARIO:
ONE DAY YOU DECIDE TO RELEASE YOUR PET HOMING PIGEONS IN THE PARK. PUTTING THE CAGES IN THE CAR, YOU DROVE TO THE PARK TRAVELING SOUTH, THEN EAST, THEN SOUTH,AND FINALLY EAST AGAIN.

FOR THE RIGHT TRIANGLE FORMULA, PLEASE DEFINE THE TWO LEGS AS TWO INDEPENDENT VARIABLES, THEN USE THE VARIABLES TO EXPRESS THE HYPOTENUSE.
Now, we have ALL the answers accept the expression for the "distance the pigeons flew home" (hypotenuse). PLEASE HELP!!
Total distance the car has driven south/north A
Total distnace the car has driven east/west B
Distances the pegions flew to return home ????
(This is a cognitive tuter program done via the internet. It will not let us go any further until we complete this blank. When we ask for a hint we get this: Please write a formula using the variable A and B to express the distances the pigeons flew to return home. In a right triangle, if the lengths of two legs are A and B, the hypotonuse is equal to the square root of (A*A+B*B)
PLEASE PLEASE HELP!! THANKS
Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
You can draw the right triangle as follows:
The total north-south distance, A, is one leg of this triangle.
The total west-east distance, B, is the other leg and this, of course, is perpedicular the first leg, A.
The straight-line distance from the start of the trip to the finish is the hypotenuse of the right triangle.
You can express distances A and B as a function of the hypotenuse, which we'll call C, using a form of the well-known Pythagorean theorem:

Now, assuming that the pigeon took the direct route home...as the crow flies, so to speak, its route would be traced by the hypotenuse of the right triangle, or C.
The pigeon flew a distance of: