Question

length of the diagonal of a rhombus is in the ratio 4 : 3 if its area is 384 CM. Find its side

Answer 1

Hey mate! Here is your answer.

Ratio of the length of diagonals =4:3
Let the diagonals be 4x and 3x
Area = 1/2 x product of diagonals
384 = 1/2 x 4x x 3x
384= 6x^2
384/6=x^2
64=x^2 =>x=8cm
So, the diagonals are 4×8 and 3×8 i.e. 32 and 24.
Half the length of the diagonals and side of a rhombus forms a right angled triangle.
so 1/2×32= 16
and 1/2 ×24= 12
Let side of the rhombus be a cm
a^2 =16^2 + 12^2
a^2= 256 +144
a^2 = 400
a = 20
Hence, the side of rhombus = 20cm

Hope it will work
Please mark it brainliest mate

Answer 2

Answer:

Answer:

Here ,

Let Diagonal 1 (d₁ ) = 4x

And Diagonal 2 (d₂ ) = 3x

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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