Question 121999: A rectangular play enclosure for some dogs is to be made with 60m of fencing using the kennel as one side of the enclosure. Algebraically determine the quadratic function that models the area of the enclosure and use it to find the dimensions that produce the maximum area.
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! MOST TEACHERS DON'T HAVE THE OPPORTUNITY NOR THE INCENTIVE TO FIND ADDITIONAL SIMPLE SOLUTIONS TO MANY MATH PROBLEMS. tHEY ARE RESTRICTED TO A DEFINED TEXT BOOK WIT A SINGLE METHOD. WE VOLUNTEERS (EX. ENGINERES, STATISTICIANS, COMPUTER SPECIALISTS, CARPENTERS, ETC.) HAVE MANY DIFFERENT SPECIALITIES THAT FORCE US TO FIND THE SIMPLEIST & MOST EFFICIENT SOLUTION TO MANY REAL PROBLEMS NOT JUST CLASS ROOM EXERCISES. ALSO, TOO MANY MATH TEACHERS ARE NOT QUALIFIED NOR CERTIFIED TO TEACH MATH & CAN THEREFORE ONLY RELY ON WHATEVER THEY CAN 'LEARN FROM THE TEXT BOOKS'.
MOST OF THESE VOLUNTEERS I'D GUESS ARE FORMER PROFESSIONAL PEOPLE AS OPPOSED TO TEACHERS. THEREFORE YOU'LL GET MANY DIFFERENT METHODS TO SOLVE A PROBLEM. MANY MANY MATH PROBLEMS HAVE AT LEAST 3 DIFFERENT MATHODS TO SOLVE THEM. MY BROTHER, A RETIRED MATH TEACHER, TAUGHT ME ALL THE METHODS HE LEARNED IN 35 YEARS OF MIDDLE & HIGH SCHOOL TEACHING.
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HAVING SOLVED MANY OF THESE 3 SIDED RECTANGLES FOR MAXIMUN AREA I'VE FOUND THE PROPORTION TO BE 1-2-1=4
60/4=15. THUS YOU HAVE 15-30-15.
15*30=450M^2 IS THE MAX AREA.
PROOF:
REDUCE THE SHORT SIDE BY 1 M.
14-32-14
14*32=448
REDUCE THE LONG SIDE BY 1 M.
15.5-29-15.5
15.5*29=449.5
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