Question

In a rhombus, whose area is 144 cm2, one of its diagonal is twice as long as
the other. The lengths of its diagonals are
[A] 24 cm, 48 cm
[B] 12 cm, 24 cm
[C] 6√2 cm, 12√2 cm
[D] 6 cm, 12 cm​

Answer 1

Answer:

(A) 24cm ,48cm

Good morning

Answer 2

Let the diagonals be x and 2x cm.

Formula for area of rhombus:- product of diagonals /2

$\frac{x \times 2x}{2} = 144 \\ \frac{2 x^{2} }{2} = 144 \\ 2x^{2} = 144 \times 2 \\ 2 {x}^{2} = 288 \\ {x}^{2} = \frac{288}{2} \\ {x}^{2} = 144 \\ x = \sqrt{144} \\ x = 12 \: cm$

x=12cm

2x=24 cm

It's option 12 and 24