Q1 A wire of 80cm long is cut into two pieces.Each piece of wire is bent to form a square.
a) Suppose the lenght of a side of one of the squares is xcm,express the total area of the two squares in terms of x.
b) Find the lengths of a side of the two squares so that the total area of the two squares is a minimum.
請列清楚步驟及答案，thz!
mathematics questions
2007-10-11 1:03 am
回答 (1)
2007-10-11 1:44 am
✔ 最佳答案
a) The perimeter of the square = 4xSo,, the perimeter of the other square = 80 - 4x
Sum of area of squares
= x^2 + [(80 - 4x)/4]^2
= x^2 +(20 - x)^2
= 2x^2 - 40 x + 400
b)
Sum of area of squares = 2(x^2 - 20x + 200)
= 2(x^2 - 20x + 100) + 300
= 2(x - 10)^2 + 300
So the sum of area is a minimum when x = 10
So the lengths of the squares are 10, (80 - 40)/4 = 10
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