Question

The diagonals of a rhombus are in the ratio 3:4.The longer diagonal is 12 cm. Find the area of rhombus.

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Answer 1

$\bf \huge {\underline {\underline \red{AnSwEr}}}$

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Given

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• Ratio of diagonals of rhombus = 3 : 4

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• Longer diagonal = 12cm

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To Find

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• Area of rhombus

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Solution

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Let the diagonals be 3x and 4x.

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d₁ = 3x

d₂ = 4x [ Longer diagonal ]

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According to question,

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Longer diagonal = 12

4x = 12

x = 12/4

x = 3cm.

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d₁ = 3x = 3 × 3 = 9cm

d₂ = 4x = 4 × 3 = 12cm

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Therefore, d₁ = 9cm and d₂ = 12cm

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$\bf Area\:of\:Rhombus= \frac {1}{2}\times (d₁ × d₂)$

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$\bf\implies \frac {1}{2}\times (9 × 12 )$

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$\bf\implies 9\times 6$

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$\bf\implies 54cm^2$

Answer 2

Answer:

let diagonals of rhombus ABCD are AC=3Kand BD=4K.which meet at point o.

perimeter=4×side

40/4=side

10cm.=side=AB=BC=CD=DA.

in right angle triangle AOB

OA²+OB²=AB²

(AC/2)²+(BD)²=(10)²

(25K²)/4=100

K²=16

OK=+/-4

AC=3K=3×4=12cm.

BD=4K=4×4=16cm

each side=10cm.,