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.
