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

BD = 10 units and x = 12 units.

Step-by-step explanation:

We know the diagonals of a rhombus bisect each other perpendicularly and one diagonal of a rhombus divides it into equal area sections.

Therefore, diagonal BD will divide the rhombus ABCD with area 120 sq. units into two equal parts and the area of Δ ABD will be 60 sq, units.

Now, AE is perpendicular to BD and we have

$\frac{1}{2} \times BD \times AE = 60$

⇒ BD = 10 units {As AE is given to be 12 units}

So, BD = x - 2 = 10

⇒ x = 12

Hence, BD = 10 units and x = 12 units. (Answer)

Answer 2

Answer:

X=12   BD=10

Step-by-step explanation:

It on Eg