Question : If the diagonals of a rhombus are 8 cm and 6 cm, then the square of its side is:
Option 1: $25\;\mathrm{cm^2}$
Option 2: $55\;\mathrm{cm^2}$
Option 3: $64\;\mathrm{cm^2}$
Option 4: $36\;\mathrm{cm^2}$
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Correct Answer: $25\;\mathrm{cm^2}$
Solution :
The square of the side length, $s^2= \frac{d_1^2 + d_2^2}{4}$, where $d_1$ and $d_2$ are the diagonals of a rhombus.
⇒ The square of the side length of the rhombus $=\frac{8^2 + 6^2}{4} = \frac{64 + 36}{4} =25\;\mathrm{cm^2}$
Hence, the correct answer is $25\;\mathrm{cm^2}$.
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