Question

As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E.

If AE = x + 2 and BD = 4x – 16, then the length of
AC is

Answer 1

4) 24

Explanation:

Diagonals of a rectangle are congruent and bisect each other.

AE = x + 2

BD = 4x - 16

2AE = BD

2(x + 2) = 4x - 16

2x + 4 = 4x - 16

20 = 2x

x = 10

AC = BD = 4x - 16 = 4(10) - 16 = 40 - 16 = 24

Answer: 4) 24