Question

ABCD is a rhombus. Length of the diagonal BD is half the length of AB. The perimeter of rhombus ABCD is 80 cm. Find the length of BO.

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 20 cm

Answer 1

The correct option is A 5 cm

ABCD is a rhombus.

Perimeter of the rhombus is 80 cm.
If, length of one side of the rhombus is a, then,
$\Rightarrow$ a+ a+ a+ a = 80
$\Rightarrow$ 4a = 80
$\Rightarrow$ a =$\frac{80}{4}$ = 20
Length of a side of rhombus = 20 cm.

Then, AB = 20 cm.
BD = $\frac{1}{2}$ AB
BD = $\frac{1}{2}$ $\times$ 20 = 10
BD = 10 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
$\Rightarrow$ 10 = 2 BO
$\Rightarrow$ BO =$\frac{10}{2}$ = 5 cm.

The length of BO is 5 cm.