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

x=12

BD=10

Explanation:

Answer 2

x = 22

BD = 20 units

Explanation:

The formula for the area of a rhombus can be used with the given values to write an equation that can be solved for x and for BD.

Area of a rhombus

The formula is ..

A = 1/2(d1)(d2) . . . . where d1 and d2 are the lengths of the diagonals.

Using the given values, we have ...

120 = 1/2(12)(x-2)

Solution

Dividing by 6, we find ...

20 = x -2 = BD

22 = x . . . . . . . . add 2

The value of x is 22.

The length of BD is 20.