Question

. The length of the diagonals of a rhombus is in
the ratio 4:3. If its area is 384 cm², find its side.

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Answer 1

Step-by-step explanation:

Ratio of the length of diagnols= 4:3

let the diagnols be 4x and 3x

Area=1/2*product of diagnols

384=1/2*4x*3x

384=6*^2

384/6=x^2

64=x^2

=x=8cm

So,the diagnols are 4*8 and 3*8 i.e.32 and 24

Half the length of the diagnols and side of a rhombus forms a right angled triangle.

so 1/2*32=16

and 1/2* 24=12

let side of a rhombus be a cm

a^2=16^2+12^2

a^2=256+144

a^2= 400

a=20

Hence,the side of a rhombus=20

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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 = $\frac{1}{2}$ × 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