Maths problem!?
2014-11-08 1:21 pm
The top and bottom margins of a poster are 8 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 388 square centimeters, find the dimension of the poster with the smallest area.
回答 (1)
2014-11-08 1:40 pm
h and w are the length and width, respectively, of the printed area
hw = 388
w = 388/h
height of poster = h+2·8 = h+16
width of poster = w+2·4 = w+8 = 388/h + 8
area a of poster = (h+16)(388/h + 8) = 8h + 516 + 6208/h
minimum area when da/dh equals 0
8 - 6208/h² = 0
8 = 6208/h²
h² = 776
h = √776 = 2√194 ≅ 27.86 cm
w = 388/h ≅ 13.93 cm
Those are weird numbers, so be sure to check my arithmetic.
The poster is 43.86 cm high and 21.93 cm wide.
hw = 388
w = 388/h
height of poster = h+2·8 = h+16
width of poster = w+2·4 = w+8 = 388/h + 8
area a of poster = (h+16)(388/h + 8) = 8h + 516 + 6208/h
minimum area when da/dh equals 0
8 - 6208/h² = 0
8 = 6208/h²
h² = 776
h = √776 = 2√194 ≅ 27.86 cm
w = 388/h ≅ 13.93 cm
Those are weird numbers, so be sure to check my arithmetic.
The poster is 43.86 cm high and 21.93 cm wide.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20141108052146AAOLkSn