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

ABCD is a rectangle so the diagonals are equal

AC = BD

3 (x - 2) = x + 18

3x - 6 = x + 18

2x = 24

x = 12

AC = 3 (x - 2) = 3 (12 - 2) = 3 (10) = 30

BD = x + 18 = 12 + 18 = 30

Answer

AC = BD = 30

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