Question

Diagnols AC and BD of a rhombus intersect at 'O' AO=4cm ar(ABCD)=40cm. find the length of OB

Answer 1

Ar of rhombus =1/2*D1*D2

1/2ac=1/2d1=ao

therefore D1=2*ao

=8

By substituting

40=1/2*8*D2

D2=10

1/2d2=no

5=bo

Answer 2

Given

         Length of the half of the diagonal

          of a Rhombus (AO) = 4 cm

⇒ Diagonal AC = 2  AC = 8 cm

    Also ,

             Area of the Rhombus = 40 $cm^{2}$

⇒           $\frac{1}{2}$*AC*BD = 40 $cm^{2}$

⇒           8(BD)= 80  $cm^{2}$

⇒             BD = 10 cm

Now,

        the length of OB = $\frac{BD}{2}$ cm

                                      = $\frac{10}{2}$ cm

                                      =  5 cm

∴ The length of OB is 5 cm

' Also find the attachment below'