F.5 MATHS

(a)
Total area = [x² + (x + 2)²] cm²
x² + (x + 2)(x + 1) ≥ 46
2x² + 3x + 2 ≥ 46
2x² + 3x - 44 ≥ 0
(2x + 11)(x - 4) ≥ 0
x ≤ -11/2 (rejected for x must be positive) or x ≥ 4
Hence, x ≥ 4 ...... (answer)


(b)
Length of the wire
= {4x + 2[(x + 2) + (x + 1)]} cm
= (8x + 6) cm

x ≥ 4
8x + 6 ≥ 8(4) + 6
8x + 6 ≥ 38
Minimum length of the wire = 38 cm ...... (answer)

The answer is as follows:
(a) x^2+(x+2)(x+1)=46
x^2+x^2+3x+2=46
2x^2+3x=44
2x^2+3x-44=0
(x-4)(2x+11)=0
x=4 or x=-5.5(捨去)
(b),因面積和長度皆沒有負數,所以正方形長闊是4cm,面積16平方厘米, 長方形長6cm,闊5cm,面積30平方厘米,周界22厘米。
The end

2011-01-15 10:33:34 補充：
The answer is as follows:
(a) x^2+(x+2)(x+1)>=46
x^2+x^2+3x+2>=46
2x^2+3x>=44
2x^2+3x-44>=0
(x-4)(2x+11)>=0
x>=4 or x>=-5.5(捨去)
(b),因面積和長度皆沒有負數,所以正方形長闊是4cm,面積16平方厘米, 長方形長6cm,闊5cm,面積30平方厘米,周界22厘米。
The end
參考資料