Respuesta :

HomertheGenius
Area of the rhombus is:
A = ( d1 · d2 ) / 2
In this case:
d1 = AC and d2 = BD.
d1 = AC = 2 · AE = 2 · 12 = 24
d2 = BD = x - 2.
120 = ( 24 · ( x - 2 )) / 2
120 · 2 = 24 x - 48
240 = 24 x - 48
24 x = 240 + 48
24 x = 288
x = 288 : 24
x = 12
BD = 12 - 2 = 10
Answer:
x = 12 units,  BD = 10 units.
Lanuel

The value of x and the length of segment BD is equal to 12 and 10 units respectively.

How to calculate the value of x.

Mathematically, the area of a rhombus is calculated by using this formula:

Area = 1/2(d1 × d2)

Where:

d1 and d2 are the diagonals of a rhombus.

Given the following data:

  • Area of rhombus ABCD = 120 square units.
  • AE = 12 units.
  • BD = x – 2 units.
  • AC = 2AE = 2(12) = 24 units.

Substituting the given parameters into the formula, we have;

120 = 1/2(24 × [x - 2])

240 = 24x - 48

24x = 240 + 48

24x = 288

x = 288/24

x = 12.

Now, we can calculate the length of segment BD:

BD = x – 2

BD = 12 – 2

BD = 10 units.

Read more on rhombus here: https://brainly.com/question/2456096

Otras preguntas