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Lerok [7]
2 years ago
9

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

Mathematics
1 answer:
erica [24]2 years ago
6 0

<u>Given</u>:

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.

<u>Value of x:</u>

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.

<u>Length of AC:</u>

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.

<u>Length of DB:</u>

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.

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