SOLUTION: A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it
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Question 1202890: A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
With one side 8 yards longer than the other side, what are the side lengths for the least perimeter of fencing?
____yards and ____yards
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Find all the information that is needed.
side lengths x and x+8
area of 256 square yards
x(x+8)=256, and want the smallest perimeter, p;
p=2x+2(x+8)
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either use of derivative, or help of a graphing tool
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Example problem is similar to https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.965885.html
https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.965885.html
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
Different parts of this problem are inconsistent each with other.
So REVISE your post/problem.
The "solution" in the post by @josgarithmetic is incorrect and leads you to nowhere.
His link and reference are IRRELEVANT.
So, ignore his post, for the safety and peace in your mind.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The statement of the problem is faulty.
If the area is to be 256 square yards and the length has to be 8 yards more than the width, then there is a single solution for the length and width -- and therefore a single solution for the perimeter.
Re-post, revising the statement of the problem so it makes sense.
Note if the length is 8 yards more than the width and the area is 256 square yards, the length and width are irrational numbers. Since mathematically this is a fairly elementary problem, I would think that the answer would be "nice" -- so perhaps the given area is something other than 256 square yards...?
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