In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second diagonal is ______.

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In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second diagonal is 16 cm. Explanation: In a rhombus the diagonals bisect each other at right angles. Half of the given diagonal is 6 cm, so using Pythagoras on the right triangle formed by half-diagonals and a side: 102 = 62 + (half of other diagonal)2 $\Rightarrow$ (half)2 = 100 – 36 = 64 $\Rightarrow$ half = 8 So, the full diagonal = 2 $\times$ 8 = 16 cm.

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