Question

Area of a rhombus is $256c{m}^2$. One of the diagonal is twice of the other diagonal. The sum of the diagonals is:

• A. $38cm$
• B. $48cm$
• C. $28cm$
• D. $56cm$

Answer 1

The correct option is B $48cm$

Let $x$ cm be first diagonal and $2x$ cm be second diagonal

Area of rhombus$=\frac{1}{2}\times$ Product of diagonals

$\therefore 256=\frac{1}{2}\times d_1\times d_2$

$⟹256=\frac{1}{2}\times \left(x\right)\times \left(2x\right)$

$⟹x^2=256$

$⟹x=\sqrt{256}$

$⟹x=16cm$

Hence the larger diagnal is $2x=2\times 16=32$

Sum of length of diagonals $=32+16=48$cm.