Answer:
BE = 21
m∠EAB = 45°
Step-by-step explanation:
The given dimensions in the rectangle are;
The length of AE = 3·x + 6
The length of CE = 6·x - 9
m∠EDA = 55°
From the properties of a rectangle, we have;
The diagonals of a rectangle bisect each other,
The lengths of the diagonals are equal
Therefore;
AC = BD
Diagonal BD bisects diagonal AC, therefore, AE = CE
Plugging in the values of AC and AE, we have;
3·x + 6 = 6·x - 9
∴ 6·x - 3·x = 6 + 9 = 15
3·x = 15
∴ x = 15/3 = 5
Therefore, we have;
AE = CE = 3·x + 6 = 3×5 + 6 = 21
AC = AE + CE = 21 + 21 = 42 = BD
BD = BE + DE and for rectangle ABCD, BE = DE
∴ BD = BE + BE = 2·BE = 42
∴ BE = 42/2 = 21
BE = 21
m∠EDA = m∠EAD = 55° by base angle of isosceles triangle ΔAED
m∠DAB = 90° = m∠EAD + m∠EAB
∴ m∠EAB = 90° - m∠EAD = 90° - 55° = 45°
m∠EAB = 45°.
