Question

If the area of a rhombus is 96 cm cube and one of its diagonal is 12 cm long, find the length of the other diagonal. Also, find its perimeter.​

Answer 1

⭐⭐⭐⭐⭐ ANSWER ⭐⭐⭐⭐⭐

                                             

We know that,

• Area of rhombus = 1/2 × product of diagonals.

Let the second diagonal be D.

So, according to the problem,

96 = 1/2 × 12 × D

=> 6D = 96

=> D= 96/6 = 16 cm.

• Side of a rhombus = √[(half of Diagonal1)^2+(half of Diagonal2)^2)]

Side of a rhombus = √(8²+6²) = √100 = 10 cm

So, Perimeter = 10+10+10+10 = 40 cm.

                                             

⭐⭐⭐ ALWAYS BE BRAINLY ⭐⭐⭐

Answer 2

$\huge\blue{Correct\:Question}$

If the area of a rhombus is 96 cm square and one of its diagonal is 12 cm long, find the length of the other diagonal.

Also, find its perimeter.

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$\huge\boxed{\fcolorbox{red}{yellow}{explanation}}$

Formula to be used :–[For Rhombus]

Area = ½ × pródúçt òf díàgóñàls

Perimeter = 4à

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Given values :·

Area = 96 cm²

Diagonal = d¹ = 12cm

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Let the other diagonal be a .

So,we can find the other diagonal by using the area of Rhombus and one of the diagonal's.

≈ A = ½ × product of diagonals.

96 cm² = ½ × 12 × x

96 cm² = 6x.

96cm²/6cm = x

16 cm = x.

So,the length of other diagonal = 16cm.

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Perimeter = 4a.

In a Rhombus we can find the side ,by using the Pythagoras theorem . i.e.

Diagonal /2

16/2 and 12/2

= 8cm and 6cm.

So ,by Pythagoras theorem,

a² = b² + c²

a² = 8² + 6²

a = √(8² + 6²)

a = √(64 + 36)

a = √100

a = 10.

So ,the side of the rhombus is 10cm.

Perimeter = 4a

4 × 10.

40cm.

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$\huge\sf\bold\pink{hope\: it\: helps\: you}$${\huge{\overbrace{\underbrace{\green{thanks}}}}}$