Question

If the area of the rhombus is 68cm and one of its diagonals is 8cm,then find the perimeter of the rhombus

Answer 1

Answer:

Rhombus

Solve for perimeter

P≈37.58cm

p Diagonal

8

cm

A Area

68

cm²

Using the formulas

A=pq

2

P=4a

a=p2+q2

2

Solving forP

P=2p2+4(A

p)2=2·82+4·(68

8)2≈37.57659cm

Step-by-step explanation:

Rhombus

Solve for perimeter

P≈37.58cm

p Diagonal

8

cm

A Area

68

cm²

Using the formulas

A=pq

2

P=4a

a=p2+q2

2

Solving forP

P=2p2+4(A

p)2=2·82+4·(68

8)2≈37.57659cm

Answer 2

It is given that,

• Area of rhombus = 68 cm²

• Length of one diagonal = 8 cm

We know that,

Area of rhombus = 1/2 x Diagonal 1 x Diagonal 2

Substitute the given values. we get,

68 =  1/2 x 8 x Diagonal 2

⇒ 68 = 4 x Diagonal 2

⇒ Diagonal 2 = 68/4

∴ Diagonal 2 = 17 cm

Let ' a ' be the side of rhombus.

∵ Diagonals of rhombus are perpendicular bisector of each other.

So, we can find the side by using Pythagoras theorem.

a² = ( first diagonal/2)² + ( second diagonal/2)²

⇒ a² = ( 8/2 )² + ( 17/2 )²

⇒ a² = 64/4 + 289/4

⇒ a² = 353/4

⇒ a² = 88.5

⇒ a = √88.5

∴ a = 9.4 cm

Also, perimeter of rhombus = 4 × side

⇒ 4 × 9.4

⇒ 37.6 cm

Therefore, perimeter of the rhombus is 37.6 cm.

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