Question

If the length of one diagonal of a rhombus is 24 cm and the perimeter is 60 cm, then the length of other diagonal is

• A. 15 cm
• B. 9 cm
• C. 12 cm
• D. 18 cm

Answer 1

The correct option is D 18 cm

The length of one diagonal of a rhombus is 24 cm and the perimeter is 60 cm.
Let the sides of the rhombus be a cm each.
Then, the perimeter of the rhombus, 4a = 60 cm.
$\Rightarrow a=15cm$
Let $AO=x$ such that $AO=\frac{1}{2}AC$



Now, the diagonals of the rhombus bisect each other at ${90}^0$.
$\therefore \angle AOD={90}^0,OD={\frac{1}{2}}^{\prime }BD={\frac{1}{2}}^{\prime }24=12cm$
Thus, in $\Delta AOD$, by Pythagoras Theorem,
$A{D}^2=A{O}^2+O{D}^2$
$P(15{)}^2=(x{)}^2+(12{)}^2$
$P(X{)}^2=(15{)}^2-(12{)}^2$
$P{x}^2=(15+12)+(15-12)$
$P{x}^2=\left(27\right)\times \left(3\right)$
$P{x}^2=81$
$Px=9cm$
∴Length of the diagonal = 2x = 2 × 9 = 18 cm
Hence, the correct answer is option (4).