(a) 9 cm (b) 10 cm (c) 8 cm (d) 20 cm
Solution:
(b) 10 cm
Clarification:
We realize that,
A rhombus is a basic quadrilateral whose four sides are of same length and diagonals are opposite bisector of one another.
As indicated by the inquiry, we get,
As indicated by the inquiry,
\[AC\text{ }=\text{ }16\text{ }cm\text{ }and\text{ }BD\text{ }=\text{ }12\text{ }cm\]
∠AOB = 90°
∵ AC and BD separates one another
AO = ½ AC and BO = ½ BD
Then, at that point, we get,
AO = 8 cm and BO = 6 cm
Presently, in right calculated ∆AOB,
Utilizing the Pythagoras hypothesis,
We have,
\[\begin{array}{*{35}{l}}
~ \\
AB2\text{ }=\text{ }AO2\text{ }+\text{ }OB2 \\
\end{array}\]
\[AB2\text{ }=\text{ }82\text{ }+\text{ }62\text{ }=\text{ }64\text{ }+\text{ }36\text{ }=\text{ }100\]
\[\begin{array}{*{35}{l}}
\therefore AB\text{ }=\surd 100\text{ }=\text{ }10\text{ }cm \\
~ \\
\end{array}\]
We realize that the four sides of a rhombus are equivalent.
Hence, we get,
one side of rhombus = 10 cm.