如图,四边形ABCD的面积等于9,∠A=∠C=90°,AB=AD,求BC+CD的长,

B和D是互补的角,B = ADF
AB =AD,AEB,AFD是直角
所以 ABE ADF全等
得到AE= AF,AECF是正方形.
边长 = √9 = 3
BC+CD = EC+CF = 2*边长 =6
法2
BD² = 2a²
BD² = x² +y² = 2a² (1)
1/2 a² + 1/2 x *y = 9 (2)
(1)+(2)*4
x² +y² + 2a² + 2xy = 36 + 2a²
(x+y)² =6²
x+y =6
2
x + x(6-x) = -x² + 7x
配成平方
= -(x-7/2)² + (7/2)²
最大值 时 x = 7/2
y = 6-x = 5/2
1/2 xy = 35/8
1/2 a² = 9 - 35/8 = 37/8
a² = 37/4
a = √37/2

（1）①∵∠BAD=∠C=90°
∴∠B+∠ADSC=180
∵∠ADC+∠ADF=180°
∴∠B=∠ADF
∵AE⊥BC AF⊥CD
∴∠AEB=∠F=90°
∵AB=AD
∴⊿ABE≌⊿ADF
∴AE=AF BE=DF
∵∠AEC=∠C=∠F=90°
∴四边形AECF是正方形
∴CE=CF