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प्रश्न
Find the area of a rhombus, each side of which measures 20 cm and one of whose diagonals is 24 cm.
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उत्तर
Given:
Side of the rhombus = 20 cm
Length of a diagonal = 24 cm
We know: If `d_1` and `d_2` are the lengths of the diagonals of the rhombus, then
side of the rhombus\[= \frac{1}{2}\sqrt{d_1^2 + d_2^2}\]
So, using the given data to find the length of the other diagonal of the rhombus:
\[20 = \frac{1}{2}\sqrt{{24}^2 + d_2^2}\]
\[40 = \sqrt{{24}^2 + d_2^2}\]
Squaring both sides to get rid of the square root sign:
\[ {40}^2 = {24}^2 + d_2^2 \]
\[ d_2^2 =1600-576=1024\]
\[ d_2 =\sqrt{1024}=32 cm\]
∴ Area of the rhombus \[=\frac{1}{2}(24 \times 32) = 384 {cm}^2\]
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