The diagonals of a rhombus ABCD intersect at oh if angle a DC is equal to 120° and OD is equal to 6 cm find or a D and side AB and perimeter of the rhombus ABCD
Answers
Answer:
ADC + ∠DAB = 180 (opposite sides of a rhombus)
120 + ∠DAB = 180
∠DAB = 180 - 120 = 60º
FInd DB:
BD = OD = 6 cm
DB = 6 x 2 = 12 cm
Define x:
Let the length of side AB = x
The length of side AD = x (All sides of a rhombus are equal)
Solve x:
BD² = AB² + AD² - 2(AB)(AD)Cos(∠DAB)
12² = x² + x² - 2(x)(x) Cos(60)
144 = 2x² - 2x²(0.5)
144 = x²
x = √144
x = 12 cm
Find side AB:
AB = x
AB = 12 cm
Find the perimeter:
Perimeter = 4 x sides
Perimeter = 4 x 12
Perimeter = 48 cm
Answer: (i) 60º (ii) 12 cm (iii) 48 cm
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