A) 12 cm
B) 9 cm
C) 15 cm
D) 8 cm
Correct Answer: C
Solution :
Let ABCD be a rhombus in which diag AC = 24 cm and diag BD =18 cm. We know that the diagonals of a rhombus bisect each other at right angles. |
\[\therefore \] \[OA=\frac{1}{2}AC=\left( \frac{1}{2}\times 24 \right)\,\,\text{cm}=12\,\,\text{cm}\] |
\[OB=\frac{1}{2}BD=\left( \frac{1}{2}\times 18 \right)\,\,\text{cm}=9\,\,\text{cm}\] |
\[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{9}^{2}}=(144+81)=225\] \[\therefore \]\[AB=\sqrt{225}=15\,\,\text{cm}\] |
\[\therefore \]Each side of the rhombus is 15 cm. |
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