SOLUTION: While standing in line for the water fountain, Mateo sees his lab partner 36 feet ahead of him and his best friend 77 feet to his right. Mateo wants to go ask his lab partner a que

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Question 1205430: While standing in line for the water fountain, Mateo sees his lab partner 36 feet ahead of him and his best friend 77 feet to his right. Mateo wants to go ask his lab partner a question, then go chat with his friend, and finally return to the water fountain line. How far will Mateo have to walk in all?
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: 198 feet

Explanation

Draw a right triangle with corner points M, P, and F.
M = Mateo's starting location
P = lab partner's location
F = the friend's location

P is directly above M.
F is to the right of M.
The 90 degree angle is at point M.
Side MP = 36 feet
Side MF = 77 feet
Hypotenuse PF is unknown, but we can use the Pythagorean theorem to solve for it.
a%5E2+%2B+b%5E2+=+c%5E2

%28MP%29%5E2+%2B+%28MF%29%5E2+=+%28PF%29%5E2

PF+=+sqrt%28%28MP%29%5E2+%2B+%28MF%29%5E2%29

PF+=+sqrt%28%2836%29%5E2+%2B+%2877%29%5E2%29

PF+=+sqrt%287225%29

PF+=+85
The hypotenuse is 85 feet.
This is the distance from the lab partner (P) to the friend (F).

Mateo walks 36 feet ahead of his initial location to talk to his lab partner. Then walks another 85 feet to talk to his friend. Lastly, he walks the remaining 77 feet to get back to his initial location in line.
That's a total of 36+85+77 = 198 feet
Note how this is the perimeter of the right triangle MPF.