Question

In the figure below is represented the rhombus ABCD with BD = 18 cm and the angle CAD = 30°. The perimeter of the rhombus ABCD is equal to:
a) 36 cm
b) 72 cm
c) 36 radical of 2
d) 54 cm
​

Answer 1

OD = BD/2 = 18/2 = 9
Sin (30) = OD/AD
=> AD = sin (30)/OD
=> AD = sin(30)/9 = 18
P = 18 x 4 = 72 cm

Answer is B

I hope it’s useful

Answer 2

Answer:

B

Step-by-step explanation:

In a rhombus

• the diagonals are perpendicular bisectors of each other

then the right triangle with AD as its hypotenuse

has the side opposite ∠ CAD as BD ÷ 2 = 18 ÷ 2 = 9

using the sine ratio in this right triangle with exact value

sin30° = $\frac{1}{2}$ , then

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{9}{AD}$ = $\frac{1}{2}$ ( cross multiply )

AD = 9 × 2 = 18

In a rhombus

• the sides are congruent (equal ) , then

perimeter = 4 × 18 = 72 cm