Question

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

Answer 1

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.