ppi93gk88d的部落格

標題:

Maths功課

• 茲 字是什麼意思-
• 4月19日生果日
• LENOVO X201i Add REM

• 茲 字是什麼意思-
• 4月19日生果日
• LENOVO X201i Add REM

 

此文章來自奇摩知識+如有不便請留言告知

發問:

An iron wire of 32 cm long is cut into two pieces to form two squares.If the sum od the area of the two squares is 34cm^2,find the lengths of the two iron wire segments.

最佳解答:

Let x be the side length of the small square and y be the side length of the large square 4x+4y = 32 => x + y = 8 ----(1) x^2 + y^2 = 34 ----(2) Sub Eq(1) int Eq(2): x^2 + (8 - x)^2 = 34 2x^2 - 16x + 30 = 0 x^2 - 8x + 15 = 0 (x-3) (x-5) = 0 x = 3 or x = 5 When x = 3, from Eq(1): y= 8-3 = 5 When x = 5, from Eq(2): y=8-5 = 3 The iron wire segment length of the large square = 4x = 4(5) = 20cm The iron wire segment length of the small square = 4y = 4(3) = 12cm

其他解答:

X^2 + Y^2 = 34 ---------(1) 4X + 4Y = 32 -----------(2) From (2), X + Y = 8 X = 8 - Y -------(3) Substitute (3) into (1), (8-Y)^2 +Y^2 = 34 64 -16Y + Y^2 + Y^2 = 34 32 - 8Y + Y^2 = 17 Y^2 -8Y -15 = 0 (Y-5)(Y-3) = 0 Y= 5 or 3 When Y=5, Substitute Y into (3) X = 8-Y = 3 When Y=3, Substitute Y into (3) X = 8-Y = 5 即係兩個 square 邊長分別係 3 同 5 cm 2 iron wire segments 就係 12cm 同 20cm !!|||||4x + 4y = 32 x^2 + y^2 = 34 2008-01-15 23:43:43 補充： 4x 4y =32x = 8 - y(8-y)^2 y^2 = 34(y-3)(y-5)=0so lengths of two iron wire segments are 3 and 5