Richard C. answered • 05/15/22
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Confidence- building Algebra1 tutor with 18 years experience
Destiny B.
asked • 05/13/22A rectangular roller skating rink has no boundaries. If you were to take a 300-foot length of rope to create boundaries around the rink, what is the maximum area?
The answers are:
A. 22,500 sq ft
B. 7500 sq ft
C. 5625 sq ft
D. Not enough information
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2 Answers By Expert Tutors
Raymond B. answered • 05/13/22
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Math, microeconomics or criminal justice
C. 5625 square feet
(300/4)^2 = 75^2 = 5625 ft^2 = max area given 300 feet limit of rope
a square is the maximum area rectangle for a fixed perimeter
side of a square with 300 perimeter = 300/4 = 75 feet
75 times 75 = 5,625 ft^2
Mark M.
To my chagrin, forty years of classroom teaching and never a Gauss!
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05/14/22
Brenda D.
tutor
Trying a few experiments and reasoning sounds certainly quite useful. I wonder if the student was also learning to use quadratics at their particular stage in the class. The situation reads like it would fit well into a quadratic. Setting 150W-W^2 equal to each given area, moving it over to the proper side of the equal sign sounds like a good experiment. 22500-150W+W^2, 7500-150W+W^2, 5625-150W+W^2. one of these factors out nicely to (75-W)^2
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05/16/22
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Mark M.
How would an Algebra 1 student know that for a given perimeter a square has the maximum area?05/14/22