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

Solution:

We will use properties of diagonals of a rhombus to find the value of x.

Given, ABCD is a rhombus with diagonals AC and DB that intersect at point E.

Diagonals of a rhombus bisect each other.

AC = 2 × EC

AC = 2 × 8 = 16 units.

Area of a rhombus ABCD = 1/2 × AC × DB.

72 = 1/2 × 16 × (x - 1) [Given]

72 = 8 × (x - 1)

x - 1 = 9

x = 10 units

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x - 1. What is the value of x?

Summary:

The value of x is 10units when the area of the rhombus ABCD is 72 units and EC = 8 and DB is x - 1.