Question

One of the diagonals of a rhombus of side 20 cm is 24 cm. The length of other diagonal is equal to

• A. 36 cm
• B. 32 cm
• C. 24 cm
• D. 28 cm

Answer 1

The correct option is B

32 cm

Let ABCD be the rhombus having side 20 cm, with one diagonal BD =24 cm

In $\Delta AOB$ (diagonal bisect each other)

$OB=\frac{DB}{2}=\frac{24}{2}=12cm$

$\angle AOB={90}^{\circ }$ (diagonasl of a rhombus bisect each other at ${90}^{\circ })$

In $\Delta AOB$, applying pythagoras theorem we get

$A{B}^2=O{A}^2+O{B}^2$

$(20{)}^2=O{A}^2+(12{)}^2$

$O{A}^2=400-144$

$O{A}^2=256$

OA =16 cm

$AC=2\times OA$

AC =32 cm