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5. The area of the rhombus is 576 sq. cm and the length of one of its
diagonal is half of the lengths of the other diagonal then find the length
of the diagonals.



Answer :

sqdancefan

Answer:

  24 cm, 48 cm

Step-by-step explanation:

You want the lengths of the diagonals of a rhombus with an area of 576 cm² and one diagonal half the length of the other.

Area

The area of a rhombus is found by ...

  A = 1/2(d₁)(d₂) . . . . . where d₁ and d₂ are the lengths of the diagonals.

Here, we have d₂ = 2·d₁, so this becomes ...

  A = 1/2(d₁)(2d₁) = (d₁)²

  d₁ = √A = √(576 cm²) = 24 cm

  d₂ = 2·d₁ = 2·(24 cm) = 48 cm

The diagonals are 24 cm and 48 cm long.

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