Question

Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9
10
14
16

Answer 1

In a rhombus the diagonals are perpendicular bisectors, so E is the midpoint of both diagonals. Thus AC = 2·EC = 16. Area = (1/2)(AC)(BD) = 72, so (1/2)(16)(BD) = 72 → 8·BD = 72 → BD = 9. Given DB = x − 1, x − 1 = 9 so x = 10.