趣味的数学-124
BD是矩形ABCD的对角线。LA和MC分别垂直于BD，并把BD分为长度各为1的三部分。求矩形ABCD的面积。
【AHSME】
錯了。
b = 2/cos x = 6^(1/2)
a*b = 3 * 2^(1/2)
更閒單一點：
設 LA= MC ＝ x
因 BMC 與 CMD 像似：
x/2 = 1/x
=>
x= 2^(1/2)
a = 3^(1/2), b = (2^2 + 2)^(1/2) = 6 ^(1/2)
a*b = 3 * 2(1/2)
設 角DBC = x。
tan (x) = (1/tan x) / 2
tan ^2 x = 1/2
tan (1/2*x) = 3^(1/3) - 2 ^(1/2)
sin x = (1/3)^(1/2)
cos x = (2/3)^(1/2)
a = 1/sin x = 3^(1/2)
b = 2/cos x = (3/2)^(1/2)
