The diagonals of a rhombus are in the ratio 5 : 12 and its area is 240 cm². Find the lengths (in cm) of the diagonals.
10\(\sqrt2\) and 24\(\sqrt2\)
Let the diagonals be 5k and 12k. Area of a rhombus: \(\dfrac12\times d_1\times d_2 = \dfrac12\times5k\times12k = 30k^2\).
Setting this equal to 240: \(30k^2=240 \Rightarrow k^2=8 \Rightarrow k=2\sqrt2\).
Diagonals: \(5k=10\sqrt2\) cm and \(12k=24\sqrt2\) cm.
Hence, the diagonals measure \(10\sqrt2\) cm and \(24\sqrt2\) cm.
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