Question

ABCD is a rhombus. Length of the diagonal BD is half the length of AB. The perimeter of rhombus ABCD is 160 cm. Find the length of BO.

• A. 8 cm
• B. 5 cm
• C. 20 cm
• D. 10 cm

Answer 1

The correct option is D 10 cm

ABCD is a rhombus.

Perimeter of the rhombus is 160 cm.
If, length of one side of the rhombus is a, then,
$\Rightarrow a+a+a+a=160$
$\Rightarrow 4a=160$
$\Rightarrow a=\frac{160}{4}=40$
Therefore, the length of the side of the rhombus = 40 cm.

Then, AB = 40 cm.
BD = $\frac{1}{2}$ AB
BD = $\frac{1}{2}$ $\times$ 40 = 20
BD = 20 cm.

Since, BD is the diagonal, and the diagonals of a rhombus are perpendicular bisectors, BO = OD

$\Rightarrow$ BD = BO + OD = BO + BO
$\Rightarrow$ BD = 2 BO
$\Rightarrow$ 20 = 2 BO
$\Rightarrow$ BO =$\frac{20}{2}$ = 10 cm.

Therefore, the length of BO is 10 cm.