Question

1. if ae = 6x - 55 and ec = 3x - 16, find db.

Explanation:

Step1: Set AE equal to EC

In a rectangle, diagonals bisect each other, so $AE = EC$.
$6x - 55 = 3x - 16$

Step2: Solve for x

Subtract $3x$ from both sides, then add 55 to both sides.
$6x - 3x = -16 + 55$
$3x = 39$
$x = 13$

Step3: Calculate length of AE

Substitute $x=13$ into $AE = 6x - 55$.
$AE = 6(13) - 55 = 78 - 55 = 23$

Step4: Find length of AC

Diagonal $AC = 2 \times AE$.
$AC = 2 \times 23 = 46$

Step5: Relate AC to DB

In a rectangle, diagonals are equal, so $DB = AC$.
$DB = 46$

Answer:

46