Question

The perimeter of a rhombus is equal to the perimeter of square. If length of diagonal of square is $20\sqrt{2}$ cm and one of the diagonals of rhombus is 32 cm then area of rhombus is

• A. $480{\text{cm}}^2$
• B. $384{\text{cm}}^2$
• C. $360{\text{cm}}^2$
• D. $420{\text{cm}}^2$

Answer 1

The correct option is B $384{\text{cm}}^2$

Answer (3)
Length of diagonal of a square of side 'a' is $\sqrt{2}a$
According to question, $\sqrt{2}a=20\sqrt{2}$
$a=20cm$

As shown in figure, side of rhombus $=20\text{cm}$
Let, $AC=32\text{cm}$
$\Rightarrow AO=16\text{cm}$
Applying pythagoras theorem in $\Delta AOB,$ we get
$O{B}^2=A{B}^2-A{O}^2={20}^2-{16}^2={12}^2$
$OB=12\text{cm},orBD=24\text{cm}$
Area of rhombus $=\frac{1}{2}\left(AC\right)\left(BD\right)=\frac{1}{2}\times 32\times 24=384{\text{cm}}^2$