In rectangle ABCD, parallel lines k and m through A and C are perpendicular to diagonal BD and divide it into three equal segments of 1. What is the area of rectangle ABCD?
The square is a rectangle too !!!
If BD = 3 then [ABCD] = 4.5 square units
AD = a AB = b BD = c
b = sqrt(9 - a2)
AM = sqrt(a2 - 1) (AM is the height of triangle ADM)
BD * AM = a * b
3[sqrt(a2 - 1)] = a[sqrt(9 - a2)]
a = √3 b = √6
[ABCD] = 3√2