Question

A person is going to start a small rectangular garden using his house as one side and his garage as another side. He has 40 m of fencing and wants to enclose a maximum area of 200 square meters. How long will the longest side of his fence be?

Answer 1

I assume the house and the garage walls make a right-angle, and also assuming he uses all of his 40m of fencing. Then one side is x, and the other side is (40-x), such that Area=x(40-x)=200.
Can you now solve for x?

Note: The minimum fence required for 200sqm is 14.142m each side, or 28.284m. That is why I assume he wants to use up the fence.

Answer 2

i did whole x(40-x)=200 thing but there's an answer key and the answer is supposed to be 20m.
also i got x= 20 +/- 10sqrt(2)

Answer 3

Could you check if the question complete?

Answer 4

what do you mean "if the question complete"?

Answer 5

I meant "if the question is complete", or if there are other constraints, or if there are typos.

Answer 6

As it is, the longest side could be as long as 34.142 m (as you have found), or 20, or as short as 14.142 to get an area of 200 sq.m. Is there a diagram that shows that the house or the garage is 20m long?

Answer 7

i checked- the question is complete/accurate and there is no diagram given

Answer 8

i thought that the house and garage would be assumed to be "infinitely long" / longer than would be needed for the rectangular garden, so that the fencing just wouldn't span as long as the house/garage it would span a section of each

Answer 9

That is a correct assumption if the lengths are not specified.
At this point I do not know why the answer was 20m, although according to my interpretation of the question, any length between 14.42 and 34.142 is equally valid.

Answer 10

...but it says the longest side of the fence

Answer 11

so that would be 20 + 10sqrt(2)

Answer 12

In correct English it would be the "longer" side of the fence when comparing two sides.
If it says "longest" side of the fence, it gives the impression that it requires the longest possible side, which you correctly calculated as 34.142 (corr. width 5.858).

Sorry, I do not know why the key give 20. Perhaps the question was changed since the key was made, perhaps the author for the key mis-interpreted the question, or there was a typo.

Answer 13

well it was a multiple choice question and the choices were 10, 20, 25, 30 and 35. none of which seem to be correct...

Answer 14

i think my teacher made a mistake

Answer 15

This is possible. Teachers are human too!
It could be that he improved the question but forgot to change the answers.

Answer 16

no that's not it there's a sheet with the question and answer that were made at the same time. it's okay i understand the problem and everything so thanks anyway :)

Answer 17

yw! :)