Given:
Given that ABCD is a rectangle.
The diagonals of the rectangle are AC and DB.
The length of AE is (6x -55)
The length of EC is (3x - 16)
We need to determine the length of the diagonal DB.
Value of x:
The value of x can be determined by equating AE and EC
Thus, we have;
[tex]AE=EC[/tex]
Substituting the values, we get;
[tex]6x-55=3x-16[/tex]
[tex]3x-55=-16[/tex]
[tex]3x=39[/tex]
[tex]x=13[/tex]
Thus, the value of x is 13.
Length of AC:
Length of AE = [tex]6(13)-55=78-55=23[/tex]
Length of EC = [tex]3(13)-16=39-16=23[/tex]
Thus, the length of AC can be determined by adding the lengths of AE and EC.
Thus, we have;
[tex]AC=AE+EC[/tex]
[tex]AC=23+23[/tex]
[tex]AC=46[/tex]
Thus, the length of AC is 46.
Length of DB:
Since, the diagonals AC and DB are perpendicular to each other, then their lengths are congruent.
Hence, we have;
[tex]AC=DB[/tex]
[tex]46=DB[/tex]
Thus, the length of DB is 46.
