現有一長68cm的鐵線折成二段,然後把各段屈折成二個正方形,已知二個正方形大小不一,而他們所圍的面積的總和是164cm二次方,設小的正方形的邊長為是x cm
a)以x表示小正方形的邊界總長和面積
b)以x表示大正方形的邊界總長和面積
c)求大正方形的邊長
請快回答 ,要考試*
2007-01-12 7:43 am
回答 (2)
2007-01-12 8:33 am
✔ 最佳答案
Let the length of the smaller square = x cm(a)
For the smaller square
Perimater = 4x cm
Area = x^2 cm^2
(b)
For the bigger square
Perimeter = (68 - 4x) cm
Side length = (68 - 4x) /4 = (17 - x) cm
Area = (17 - x)^2 cm^2
(c)
Consider the area of the 2 squares
x^2 + (17 - x)^2 = 164
x^2 + 289 - 34x + x^2 - 164 = 0
2x^2 - 34x + 125 = 0
Apply quadratic formula, we get
x = 11.62 or x = 5.38 (rejected, since 17 - x must be smaller than x)
17 - x
= 17 - 11.62
= 5.38
Hence, side length of bigger square = 11.62 cm (correct to 2 decimal places)
參考: me
2007-01-12 7:49 am
a. 4x=邊長 x^2=面積
b. (68-x)x4=邊長 , (68-x)^2=面積
c. 教哂你喇,最後一步自己來啦^^
b. (68-x)x4=邊長 , (68-x)^2=面積
c. 教哂你喇,最後一步自己來啦^^
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