Question

The diagonals of a rhombus ABCD intersect at O. If ∠ADC = 120° and OD = 6 cm, find :(i) ∠OAD(ii) side AB(iii) perimeter of ABCD

Answer 1

Answer:

(i) 60º (ii) 12 cm (iii) 48 cm

Step-by-step explanation:

Find ∠OAD

∠OAD = ∠OCD (Isosceles triangle)

∠OAD = (180 - 120) ÷ 2

∠OAD = 30º

Find side ∠DAB:

∠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

Answer 2

Answer:

I. 60deg

II. 12 cm

III. 48 cm

Step-by-step explanation:

You can do it practically