Question

the area of rhombus is 2016cm²and its side is 65cm.find it's diagonal?​

Answer 1

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Step-by-step explanation:

Let the diagonals of the rhombus be 2x and 2y

Area of rhombus =

2

1

× Product of the diagonals

=

2

1

×2x×2y=2xy

⇒2xy=2016

⇒xy=1008

Also,

x

2

+y

2

=65

2

⇒x

2

+y

2

−2xy=4225−2xy

⇒(x−y)

2

=4225−2016

⇒(x−y)

2

=2209

∴(x−y)=47 (1)

similarly,

we can find (x+y)

2

=6241

∴x+y=79 (2)

Solving (1) and (2) we get,

x=63 and y=16

Now, the diagonals are 2x and 2y

so, the length of the diagonals is 126cm and 32cm.