Question

the area of a rhombus is 138 CM square if one of the diagonal is 11.5 cm long find the length of other diagonal

Answer 1



Mansi Shah asked in Math

the area of a rhombus is 216 cm sq if its one diagonal is 24 cmfind
(i) the length of its other diagonal
(ii) length of its side
(iii)perimeter of rhombus

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Answer :

We have our rhombus ABCD .

Given diagonal AC  =  24 cm
And
Area of rhombus  ABCD  =  216 cm2
And
 

we know Area of rhombus  =  , So


And
So,
Length of other diagonals  =  18 cm                              (  Ans ) 

ii ) We know diagonals of rhombus are perpendicular bisectors to each other , So we get
and OA =  OC  =  12 cm and OB  =  OD  =   9  cm

Now we apply Pythagoras theorem in triangle AOB

AB2 =  OA2 + OB2

AB2 =  122  + 92

AB2 =  144  + 81

AB2  = 225

AB  =  15 cm

So,

Length of side of rhombus  =  15 cm                                ( Ans )

iii )  We know perimeter of rhombus  =  4 (  Side of rhombus  )
So,
Perimeter of rhombus  ABCD  =  4 ( 15 ) =  60 cm                                       ( Ans )