ABCD is a rectangle. find the length of each diagonal. AC= 3(x-2) and BD=x+18 what is AC? What is BD?

The length of the diagonals of the rectangle are AB = 30 and BD = 30

What is a rectangle?

A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also, the opposite sides are parallel and of equal length.

Given that, ABCD is a rectangle and its diagonals are  AC= 3(x-2) and BD=x+18

According to the property of a rectangle,

Diagonals of a rectangle are equal.

Therefore, AC = BD

3(x-2) = x+18

3x-6 = x+18

2x = 24

x = 12

AC = 3(12-10) = 30

BD = 12+18 = 30

Hence, the diagonals of the rectangle are AB = 30 and BD = 30

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The diagonals of a rectangle are congruent. That means that their lengths are equal. One diagonal is AC, and the other diagonal is BD. AC must equal BD. We set their lengths equal and solve for x.

3(x - 2) = x + 18

Distribute the 3 on the left side.

3x - 6 = x + 18

Subtract x from both sides; add 6 to both sides.

2x = 24

Divide both sides by 2.

x = 12

Now that we know x = 12, we replace x with 12 in BD = x + 18 to find the length of BD.

BD = x + 18 = 12 + 18 = 30

Since the diagonals are congruent, the length of AC is also 30.

Answer:   AC = 30;  BD = 30