ABCD is a rectangle. Find the length of each diagonal.
AC = 2(x – 3)
BD = x + 5
2
11
8
16
Let the length of the rectangle be x units.
Since ABCD is a rectangle, AC and BD are the diagonals.
Given: AC = 2(x – 3) and BD = x + 5.
Since the diagonals of a rectangle are congruent, we can set the two diagonals equal to find the value of x:
2(x – 3) = x + 5
2x – 6 = x + 5
x = 11
Now that we have found the value of x, we can find the length of the diagonals:
AC = 2(x – 3) = 2(11 – 3) = 2(8) = 16
BD = x + 5 = 11 + 5 = 16
Therefore, the length of each diagonal is 16 units.
Answer: 16