Question : The parallel sides of a trapezium are $8\;\mathrm{cm}$ and $4\;\mathrm{cm}$. If the $\mathrm{M}$ and $\mathrm{N}$ are the mid-points of the diagonals of the trapezium, then the length of $\mathrm{MN}$ is:
Option 1: $12\;\mathrm{cm}$
Option 2: $6\;\mathrm{cm}$
Option 3: $1\;\mathrm{cm}$
Option 4: $2\;\mathrm{cm}$
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Correct Answer: $2\;\mathrm{cm}$
Solution :
In a trapezium, the line segment joining the mid-points of the diagonals is parallel to the bases and its length is half the difference of the lengths of the bases.
Given that the lengths of the parallel sides (bases) are $8\;\mathrm{cm}$ and $4\;\mathrm{cm}$.
The length of the line segment $\mathrm{MN}$ $=\frac{1}{2}(8-4) = 2 \text{ cm}$
Hence, the correct answer is $2\;\mathrm{cm}$.
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