MC....MATHS

ans:

設 y 是周界

AB=(y/2)[3/2+3] = 3y/10
BC=(y/2)[2/2+3] = 2y/10
PQ=(y/2)[4/4+3] = 4y/14
QR=(y/2)[3/4+3] = 3y/14

ABCD的面積: PQRS 的面積 =

=AB * BC : PQ * QR

= 3y/10 * 2y/10 : 4y/14 : 3y/14

= 49:50

很好..

另外, sandshrew_0813_brian, 如果你這樣直接寫出2個長方形的周界可能性是不太好的(雖然你岩了), 考試時拎唔足分, 別人理解上也難一點。

設 X 是周界

AB=(X/2)[3/2+3] = 3X/10
BC=(X/2)[2/2+3] = 2X/10
PQ=(X/2)[4/4+3] = 4X/14
QR=(X/2)[3/4+3] = 3X/14

ABCD的面積: PQRS 的面積 =

=AB * BC : PQ * QR

= 3X/10 * 2X/10 : 4X/14 : 3X/14

= 49:50

2008-01-29 23:52:41 補充：
考試如果要做 working steps, 不要代真數計算, 因為改卷既多數都唔比分

For simple calculation,
Let the perimeter of the two rectangles be 14 units
As AB:BC =3:2 and PQ:QR = 4:3,
AB = 4.2 units and BC = 2.8 units
PQ = 4 units and QR = 3 units
Area of ABCD = 4.2 x 2.8 = 11.76 sq units
Area of PQRS = 4 x 3 = 12 sq units
ABCD的面積 : PQRS 的面積 = 11.76 : 12 = 1176 : 1200 = 49 : 50


2008-01-29 23:59:58 補充：
The above steps are suitable enough when you are doing MCs, and it is for your better understanding. Don't be worried as if this question is a long question, sub-questions will be given to guide you to the answer.

AB:BC=3:2=12:8
PQ:QR=4:3=12:9

ABCD:PQRS=12x8：12x9=8：9