A fence is to enclose a lot with area 100 square meters. The front of the fence (considered the east-west side) is bounded by a road and requires no fence. Fencing for the back (also the east-west side) is Sm per meter. Both north-south sides cost $2 per meter (a) What dimensions minimize cost? (b) How much longer are the east-west sides (i.e., what is the ratio east-west lengths over the north-south lengths)? Hint it may be helpful to first attempt the problem with a specific value of m, say for example m 2 for scratch work, to see a pattern for general m.
A fence is to enclose a lot with area 100 square meters. The front of the fence (considered the east-west side) is bounded by a road and requires no fence. Fencing for the back (also the east-west side) is Sm per meter. Both north-south sides cost $2 per meter (a) What dimensions minimize cost? (b) How much longer are the east-west sides (i.e., what is the ratio east-west lengths over the north-south lengths)? Hint it may be helpful to first attempt the problem with a specific value of m, say for example m 2 for scratch work, to see a pattern for general m.
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter8: Areas Of Polygons And Circles
Section8.CR: Review Exercises
Problem 40CR
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Transcribed Image Text:A fence is to enclose a lot with area 100 square meters. The front of the fence
(considered the east-west side) is bounded by a road and requires no fence. Fencing
for the back (also the east-west side) is Sm per meter. Both north-south sides cost
$2 per meter
(a) What dimensions minimize cost? (b) How much longer are the east-west sides
(i.e., what is the ratio east-west lengths over the north-south lengths)? Hint
it may be helpful to first attempt the problem with a specific value of m, say for
example m 2 for scratch work, to see a pattern for general m.
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