Question

perimeter of a rhombus is 64 cm and its height is 6 CM if length of its one diameter is 16 cm then the length of the diameter is​

Answer 1

Step-by-step explanation:

let abcd is a rhombus.

we know that the adjecent side of rhombus are equal.

so, ab+bc+cd+ad=64cm

so 4ab=64

=>ab=16cm

:.ab=bc=cd=ad=16cm

we know that the diagonals(diameter) bisector each at 90°.

so let the point of intersection be O and the diameter bc=16cm

now in triangle AOB,

using pythagoras theorm,

AB²=(OA)²+(OB)²

16²=(OA)²+8²-------[1/2BC=OB]

256=(OA)²+64

256-64=(OA)²

192=(OA)²

OA=root192

the AD=OA+OD

2root192(ans)