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The length of the diagonals of a rhombus are 24 cm and 10 cm find the side of a

Posted by Somnath Chakrabarti 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 5 months ago

Let ABCD be the rhombus where AC = 10 cm and BD = 24 cm.

Let AC and BD intersect each other at O.

Now, diagonals of rhombus bisect each other at right angles.

Thus, we have
AO = 1/2 AC = 1/2 (10) = 5 cm and
BO = 1/2 BD = 1/2 (24) = 12 cm

Since AOB is a right angled triangle, by Pythagoras theorem, we have
AB² = AO²+ BO²
AB² = 5² + 12² = 25 + 144 = 169
Hence, AB = 13

Thus, length of each side of rhombus is 13 cm.

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