The length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.
What is diagonal?
" Diagonal is defined as the length between the opposite vertices of the given polygon."
Formula used
Cosine law
[tex]a^{2} =b^{2} +c^{2} -2bc Cos A[/tex]
According to the question,
In the given parallelogram PQRS
In ΔPQS
PQ = 6units
PS = 4 units
QS = x units
∠QPS = 55°
Apply cosine law to get the length of the diagonal we have,
[tex]x^{2} = 6^{2} +4^{2} -2(6)(4)Cos 55\°[/tex]
⇒ [tex]x^{2} = 36 +16 -48( 0.5736)[/tex]
⇒[tex]x^{2} = 24.4672[/tex]
⇒[tex]x= 4.946[/tex]
⇒ x≈5 ( nearest whole number)
Hence, the length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.
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