Question

Rhombus A B C D is shown. All sides are congruent. Lines are drawn from point A to point C and from point D to point B and intersect at point E at the center.

The area of rhombus ABCD is 120 square units.
AE = 12 and BD = x – 2. What is the value of x and the length of segment BD?

x =

BD =
units

Answer 1

Area = (AC * BD) / 2 = 120, and AE = 12 so AC = 24.
Thus 24 * BD = 240 → BD = 10.
Since BD = x − 2, x − 2 = 10 → x = 12.

x = 12
BD = 10 units