F.4 MATHS......... 急用..!

2(x+y)=20.....(1)
(x+2)(y+2)=2xy.....(2)

from (1),
x+y=10
y=10-x.....(3)

substitute (3) into (2)
(x+2)(10-x+2)=2x(10-x)
-x^2+10x+24=20x-2x^2
x^2-10x+24=0
(x-6)(x-4)=0
x=6 or x=4

x=6, y=4 or
x=4, y=6

Let A(cm^2) be the area of the rectangle.

Then, xy = A. ---------- (1)

"If the length and the width are both increased by 2cm,the area of the
new rectangle will double the original one."
==> (x + 2)(y + 2) = 2A
==> xy + 2(x + y) + 4 = 2A ---------- (2)

"the perimeter is 20cm" ==> 2(x + y) = 20 ---------- (3)

Then, sub. (1) & (3) into (2) : A + 20 + 4 = 2A ==> A = 24 --- (4)

From (1) & (4) : xy = 24 ---------- (5)
From (3) : x = 10 - y ---------- (6)

Sub. (6) into (5) :
(10 - y)y = 24
y^2 - 10y + 24 = 0
y = 4 or y = 6 ---------- (7)

Sub. (7) into (6) : x = 6 when y = 4 or x = 4 when y = 6.

Therefore, the dimensions of the rectangle are (6 * 4) cm^2.

2(x + y) = 20
(x + 2)(y +2) = 2xy

x + y = 10
xy = 24

x = 4 and y= 6
or
x = 6 and y= 4