Question

the length of the diagonals of a rhombus is in the ratio 4:3. If it's area is 384 cm2. Find it's side.

Answer 1

Let the diagonals be 4a and 3a

Area = D1 × D2 / 2

=> 384 = ( 4a) (3a) / 2

=> 384 = 6a^2

=> 64 = a^2

=> a = 8

D1 = 32 cm

D2 = 24 cm

Now,

Side = sqrt [ (D1/2)^2 + (D2 / 2)^2]

= sqrt ( 16^2 + 12^2)

= sqrt ( 256 + 144)

= sqrt ( 400)

= 20 cm

Side of rhombus = 20 cm

Answer 2

Answer:

Here ,

Let Diagonal 1 (d₁ ) = 4x

And Diagonal 2 (d₂ ) = 3x

_____________________

As we know that

Area of a rhombus = $\frac{1}{2}$× d₁ ₓ d₂

→ 384 =  × 4x × 3x

→ 384 × 2 = 12x²

→ 768 = 12x²

→ x² =   $\frac{768}{12}$

→ x² = 64

→ x = √64

→ x = 8

__________________

Then ,

d₁ = 4x = 4 × 8 = 32 cm

d₂ = 3x = 3 × 8 = 24 cm

________________

In each triangle formed in the rhombus the length of diagonals will become half

Let the side be y

By pythagoras theorm :

16² + 12² = y²

256 + 144 = y²

y² = 400

y = √400

y = 20 cm