A metal wire of length 80 com is cut into two parts so that one part is 4k cm long. Now each of the two parts of metal wire is bent to form a square. Find the value of k so that the sum of the areas of the two squares formed is a minimum.
P.S. I don't really know the meaning about the last sentance, can you explain to me and help me to solve it?
THX!!!
F.4 Maths quadratic equation
2009-11-13 1:45 am
回答 (1)
2009-11-13 2:01 am
✔ 最佳答案
當若兩方形面積之和為最小時,k值為多小呢?一截是長4k cm
另一截是長 (80 - 4k) cm
長4k cm的折為方形後,邊長為k cm,面積 = k^2 cm^2
長(80 - 4k) cm的折為方形後,邊長為(20 - k) cm,面積 = (20 - k)^2 cm^2
兩面積之和 = k^2 + (20 - k)^2
= 2k^2 - 40k + 400 cm^2
= 2(k^2 - 20k + 100) + 200 cm^2
= 2(k - 10)^2 + 200 cm^2
當k=10時,兩面積之和為最小值(200 cm^2).
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