Question

if the rhombus is 68 cm² and one it's diagonals is 8 cm, then find the perimeter of the rhombus

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Answer 1

Correct Question :

If the area of rhombus is 68 cm² and one of it's diagonals is 8 cm, then find the perimeter of the rhombus

Answer :

Perimeter of rhombus = 37.6 cm

Step-by-step explanation :

Given,

one of the diagonals, d₁ = 8 cm

area of the rhombus = 68 cm²

Let the other diagonal be  "d₂ cm"

we know,

   $\sf Area \ of \ the \ rhombus = \frac{1}{2} d_1 d_2$

  68 cm² = 1/2 (8 cm × a cm)

   68 = 4a

    a = 68/4

    a = 17 cm

The other diagonal = 17 cm

  Let the side of the rhombus be "a cm"

we know,

    $\sf side \ of \ the \ rhombus =\frac{1}{2} \sqrt{d_1 ^2+d_1 ^2 }$

           $\sf a=\frac{1}{2} \sqrt{8^2+17^2} \\\\ a=\frac{1}{2} \sqrt{64+289} \\\\ a=\frac{1}{2} \sqrt{353} \\\\ a=\frac{1}{2} (18.79) \\\\ a \simeq 9.4 \ cm$

The side of the rhombus ≈ 9.4 cm

Perimeter of the rhombus = 4a

     ≈ 4(9.4 cm)

     ≈ 37.6 cm

Therefore, the perimeter of the rhombus is 37.6 cm