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Question
In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second diagonal is ______.
Options
20 cm
18 cm
16 cm
22 cm
MCQ
Fill in the Blanks
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Solution
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
⇒ (half)2 = 100 – 36 = 64
⇒ half = 8
So, the full diagonal = 2 × 8 = 16 cm.
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