有一塊長方形的金屬片abcd,其AC=24cm,DC=12cm,將這塊金屬片熔化後,再鑄成面積相等的正方形pqrs,金屬片的周界改變了多少?
更新1:
help!
math!畢氏定理.
2009-02-24 4:16 am
我想問一條數
有一塊長方形的金屬片abcd,其AC=24cm,DC=12cm,將這塊金屬片熔化後,再鑄成面積相等的正方形pqrs,金屬片的周界改變了多少?
有一塊長方形的金屬片abcd,其AC=24cm,DC=12cm,將這塊金屬片熔化後,再鑄成面積相等的正方形pqrs,金屬片的周界改變了多少?
回答 (2)
2009-02-24 5:08 am
✔ 最佳答案
AD^2 = AC^2 - DC^2 = 24^2 - 12^2 = 432AD = sqrt 432.
So area = AD x DC = 12 x sqrt 432 = 12 sqrt 432.
perimeter = 2(AD + DC) = 2(sqrt 432 + 12) = 65.57.
Area of square PQRS = 12 sqrt 432
therefore , side of the square = sqrt ( 12 sqrt 432) = 15.79.
Perimeter of square = 4 x 15 79 = 63.17.
So change in perimeter = 65.57 - 63.17 = decreased 2.4 cm.
2009-02-24 5:05 am
Let x be the length of the square
x^2 = 24 * 12
x = 12 * sqrt(2)
x = 16.97 cm (2 d.p.)
Change of Parameter
= 4 * 16.97 - (24+12)*2
= 67.88 - 72
= - 4.12 cm
Change of Parameter in %
= (- 4.12 / 72) * 100%
= - 5.72 %
x^2 = 24 * 12
x = 12 * sqrt(2)
x = 16.97 cm (2 d.p.)
Change of Parameter
= 4 * 16.97 - (24+12)*2
= 67.88 - 72
= - 4.12 cm
Change of Parameter in %
= (- 4.12 / 72) * 100%
= - 5.72 %
參考: Myself
收錄日期: 2021-04-25 22:48:19
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