If area of a rhombus is 225 cm2. One of the diagonal is half of the other diagonal. The sum of the diagonals would be:

If area of a rhombus is 225 cm². One of the diagonal is half of the other diagonal. The sum of the diagonals would be:

A 45 cm

B 48 cm

C 36 cm

D 144 cm

E None of these

Correct Answer: Option A

Let first diagonal is x cm, then the other one would be 2x cm

]Now, formula

Area of a rhombus = (1/2)×product of its diagonals

\(\eqalign{ & \Rightarrow 225 = \frac{1}{2} \times 2x \times x \cr & \Rightarrow {x^2} = 225c{m^2} \cr & \Rightarrow x = 15cm \cr}\)

Then the diagonals would be 15 cm and 30 cm

∴ Sum of the diagonals = 45 cm