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Question
Find the length of each side of a rhombus whose diagonals are 24cm and 10cm long.
Solution
Let ABCD be the rhombus with diagonals (AC = 24 cm and BD = 10 cm) meeting at O.
We know that the diagonals of a rhombus bisect each other at angles.
Applying Pythagoras theorem in right-angled AOB, we get:
`AB^2=AO^2+BO^2=12^2+5^2`
`AB^2=144+25=169`
`AB=sqrt169=13 cm`
Hence, the length of each side of the rhombus is 13 cm.
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