Math problem I’m stuck on *^*

Question

I really need help on this problem!!

Mr.Allen wants to build a pen as large as possible for his pigs but unfortunately he can’t afford it and can only afford 24 feet of fencing he does not want his pigs to get out so there should be no gaps of holes in the pen

1. What the largest possible pen he can make for his pigs using the fencing he has . Draw out the different fences you can crest on a graph paper

2. What shape provided the largest area for his pigs

3) Mr.Allen also has a large barn he relized he could use the side of the barn as one of the sides of his pen in order to give his pigs even more space assuming he still has 24 feet of fence what is the largest amount of space he can provide for his pigs . Draw out the different fences you create on the graph paper provided

4) did the same shape that provided the largest area for his pigs the first time match the shape when using the barn as a wall? What was different about it

5) it turns out he ended up breaking one feet worth of fencing while trying to install it . What is the largest amount of space he can provide his pigs now given he only has 23 feet of fence remaining? Assume he is still using the side of the barn as one of the sides of the pen.

Answer 1

1. Well just assume the end of the fence is 1, 2, 3 .... feet. Draw out the corresponding rectangle and find the area. Keep going until you have found the rectangle with largest area. So if the end is 1, the long side must be (24 - 2 x 1) / 2 = 11 so you draw a 11 x 1 rectangle (with area 11)
2. Use your rectangles to answer this
3. Same idea except you draw three sides of the rectangle using the fence, so if the end is 1, the long side will be (24 - 2 x 1) = 22, with an area of 22
4. You can answer that one
5. Try and relate your answer in (3) to the total length of the fence - 24. Then use this to draw a conclusion if the fence was 23 not 24. Alternatively you can draw pictures with fence of 23 and find which end length and long side gives maximum area (that's longer)