A farmer wishes to build a rectangular sheep pen with a 160m fence,using one side of an existing shed as the side.The shed is also rectangular of measurement 20m X 20m.
(a)Find the measurement and the area of the sheep if one side of the existing shed is used as the width of the sheep pen.
(b)By using the fence of the same length and using the width of the shed as part of the width of the sheep pen,find the length and width of the sheep pen with maximum area.
(c)If two sheep pens of the same size are build adjacent to each other,find
(i)the length of the new sheep pen if one side of the shed is used as the width of the sheep pen.
(ii)the length and width of the sheep pen,which is adjusted so that the enclosed area is maximum.
(d)Find the maximum enclosed area if the same fence is used to construct three rectangular sheep pens.
2006-10-14 23:01:39 · 5 answers · asked by evolutionf330q 2 in Science & Mathematics ➔ Mathematics
A farmer wishes to build a rectangular sheep pen with a 160m fence,using one side of an existing shed as the side.The shed is also rectangular of measurement 20m X 20m.
(a)Find the measurement and the area of the sheep pen if one side of the existing shed is used as the width of the sheep pen.
(b)By using the fence of the same length and using the width of the shed as part of the width of the sheep pen,find the length and width of the sheep pen with maximum area.
(c)If two sheep pens of the same size are build adjacent to each other,find
(i)the length of the new sheep pen if one side of the shed is used as the width of the sheep pen.
(ii)the length and width of the sheep pen,which is adjusted so that the enclosed area is maximum.
(d)Find the maximum enclosed area if the same fence is used to construct three rectangular sheep pens.
2006-10-14 23:14:09 · update #1
a and b) If one side of the shed is used, it means that the width of your pen is 20m So you have 160m fence to cover the pen. You know the pen's side opposite to the shed would be also 20m. Therefore, if you use all the fences you would have a rectangular pen of 20m width and 70m length. (160-20=140, 140/2=70). The area of this shed 70*20=1400m2. You can play with the length of the pen and obtain different rectangular pens but the one with 70m length would be the biggest one.
c) This time you will have to two pens with 30m length each and 20m width each (160-20-20=120, 120/4=30). One side will be used by both pens. The enclosed maximum area is 2*30*20=1200m2
d) This time you will have to three pens with 50/3m length each and 20m width each (160-20-20-20=100, 100/6=50/3=16.67). Two sides will be used commonly. The enclosed maximum area is 50*20=1000m2
2006-10-14 23:33:39 · answer #1 · answered by daniel_cohadier 3 · 0⤊ 0⤋
This can be accomplish
The length equals 60 m
The opposite Length is 20 m plus one side of the shed equals 20 meters and the opposite side of the shed another 20 m of fence. A total of 60 m.
The width are 20 m each.
2006-10-15 06:39:51 · answer #2 · answered by SAMUEL D 7 · 0⤊ 0⤋
you say that the shed is rectangular of measurement 20m*20m
wont it be a square then?
2006-10-15 07:24:58 · answer #3 · answered by raj 7 · 0⤊ 1⤋
Sounds like you need to either spend time with your textbook or with the teacher after school. Perhaps both.
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2006-10-15 06:15:33 · answer #4 · answered by lcmcpa 7 · 0⤊ 0⤋
"Find the measurement and the area of the sheep "???
It depends how much he feeds them.
2006-10-15 06:04:44 · answer #5 · answered by nnjamerson 3 · 1⤊ 0⤋