Question

If AE=6x-55 and EC=3x-16, find DB. (Hint: Find x first and then substitute.)

Answer 1

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;

$AE=EC$

Substituting the values, we get;

$6x-55=3x-16$

$3x-55=-16$

       $3x=39$

         $x=13$

Thus, the value of x is 13.

Length of AC:

Length of AE = $6(13)-55=78-55=23$

Length of EC = $3(13)-16=39-16=23$

Thus, the length of AC can be determined by adding the lengths of AE and EC.

Thus, we have;

$AC=AE+EC$

$AC=23+23$

$AC=46$

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;

$AC=DB$

 $46=DB$

Thus, the length of DB is 46.