我知道答案但唔know do-.-help..

1)兩個長方形的長和闊的比都是3:1.大長方形的闊比小長方形多4cm,大長方形的周界是小長方形的2倍.分別求兩個長方形的面積

Let Small Rectangle be Length be L and Breadth be B
Length = 3 x Breadth : L = 3B
Large Rectangle be Length be L1 and Breadth be B1
B1 = B + 4
L1 = 3 x B1 = 3 (B + 4)
Perimeter of Small Rectangle, P = 2 (L + B) = 2(3B + B) = 8B
Permeter of Larger Rectangle, P1 = 2 (L1 + B1) = 2 x ( 3(B + 4) + (B + 4) )
P1 = 8 (B + 4)
Since P1 = 2P
8 (B+4) = 2 (8B)
B = 4cm

Therefore, Small Rectangle is L=3x4cm & B=4cm
12cm x 4cm (Area = 48cm2)
Big Rectangle is L1=3 (4+4) cm & B1 = (4+4)cm
24cm x 8 cm (Area = 192cm2)

2)甲乙兩地相距550公里.陳生駕車以每小時50公里的速率從甲地往乙地.他出發半小時,李生駕車由乙地住甲地.若李生的行車速率是陳生的兩陪,問李生開出後幾小時,他們會相遇.

Distance between A and B = 550km
Chan is driving at 50km/h from A to B
Lee is driving at 2x50=100km/h from B to A

Let t be the time of interception of Mr. Chan and Mr. Lee
Distance travelled by Mr Chan at interception, d1 = 50t
Distance travelled by Mr. Lee at interception, d2 = 100 (t-0.5)
d1 + d2 = 550km
50t + 100(t-0.5) = 550
150t - 50 = 550
t = 4hrs

(問李生開出後幾小時,他們會相遇) Mr Lee started driving 0.5hr after Mr Chan
Time Mr. Lee meets Mr. Chan = 4-0.5 = 3.5hr after leaving Point B


3)中六學生參加暮捐,甲班共捐$288,乙班共捐$280.己知甲的學生比乙班的多4人,而甲班平均每人捐的$比乙班的少$1,問甲,乙兩班各有幾多人.

Class A donated $288
Class B donated $280
Student of Class A = Class B + 4
Average donation of Class A = Average donation of Class B - $1

Let Class B has X students
Class A = X + 4 students
Average Donation of Class A = Total Donation of Class A / No. of Class A Students
Average Donation of Class A = 288 / (X + 4)
Average Donation of Class B = Total Donation of Class B / No. of Class B Students
Average Donation of Class B = 280 / X
Average donation of Class A = Average donation of Class B - $1
288 / (X + 4) = 280/X -1
288 = 280 { (X + 4) / X } - (X + 4)
288X = 280 (X + 4) - X (X + 4)
288X = 280X + 1120 - X2 - 4X
X2 + 4X - 1120 = 0
X = 31.5 or -35.5 (Cannot be negative)
X = 32 (No decimal for Human)

Therefore Class A has 35 Students and Class B has 31 Students


4)把32cm長的線截成兩段,然後分別把每段扭成正方形,若兩個正方形面積之和34cm^2,求兩段線的長度 help>

Let the length of 2 strings be X and Y
X = Lcm , Y = (32-L) cm
Square made with X has sides = L / 4 cm
Square made with Y has sides = (32-L) / 4 cm
Area of Square X = L2 / 16
Area of Square Y = (32-L)^2 / 16
Area of Square X + Y = 34
L2 + (32-L)^2 = 34 x 16
L2 + (1024 + L2 - 64L) = 544
2L2 - 64L + 480 = 0
L2 - 32L + 240 = 0
L = 12 or 20

Length of X =12cm and Y=20cm

1)假設小長方形的闊度是x cm，則小長方形周界為2(3x+x)=8x cm
大長方形周界:
2*3(x+4) +2*(x+4) = 6x+24+2x+8=8x+32
已知大長方形的周界是小長方形周界2倍=16x cm
所以8x+32=16x
x=4
小長方形面積=3x*x=12*4=48cm^2
大長方形面積=3(x+4)(x+4)=192cm^2

2)李生開車時陳生己行距離=50km/hr * 0.5hr=25km
李生開車時兩者距離=550-25=525km
設李生開車後相遇時間為x小時
李生所行距離+陳生所行距離=50x+2(50x)=525km
150x=525
x=3.5

3)設乙班有學生x人，則甲班人數為x+4
甲班捐款平均值=288 / (x+4)
乙班捐款平均值=280 / x
甲班平均每人捐的$比乙班的少$1
288/(x+4) + 1 = 280/x
x=28
乙班有學生28人，則甲班人數為x+4=32人