F.2 math

a. 正方形的周界

= 長方形的周界

= (闊 + 長) X 2

= 2(a + b)

所以，正方形的邊長

=周界 / 4

= (a + b)/2 cm





b. 長比闊多6 cm

所以，a = b + 6

長方形面積

= ab

= b(b + 6)

= (b^2 + 6b) cm^2

正方形面積

= [(a + b)/2]^2

= (b + 6 + b)^2 / 4

= (4b^2 + 24b + 36) / 4

= (b^2 + 6b + 9) cm^2

所以，面積差

= (b^2 + 6b + 9) - (b^2 + 6b)

= 9 cm^2

a.
鐵線的長度
=長方形的周界
=2(a + b)

正方形邊長
=鐵線的長度 / 4
=(a + b)/2

b.
長方形的長度比闊度多6cm
a - b = 6
a = 6 + b ... (1)

長方形面積
= ab cm^2
= b (b + 6) cm^2
= (b^2 + 6b) cm^2

正方形面積
= [ (a + b)/2 ]^2 cm^2
= [ (2b + 6)/2 ]^2 cm^2
= (b + 3)^2 cm^2
= (b^2 + 6b + 9) cm^2

正方形與長方形面積的差
= [(b^2 + 6b + 9) - (b^2 + 6b) ] cm^2
= 9 cm^2

a. If the rectangular has a length of a and b, the square will have a length of
(2a + 2b)/4 = ( a + b ) /2

b. Without loss of generality, let b = a - 6
The area of the rectangular = (a) (b) = a(a-6)
The area of the square = [ ( a + b ) /2 ]^2 = ( a - 3 )^2
The difference of their area = | ( a - 3 )^2 - a(a-6) |
= 9