Question

ABCD is a rhombus whose diagonal intersect at o if a b is equal to 10 centimetre diagonal BD is equal to 16 centimetre find the length of the diagonal AC​

Answer 1

Diagonals of the rhmbus bisect each other at right angles. BO = BD/2 = 16/2 = 8. Therefore, ΔAOB is a right angled triangle. According to Pythagoras theorem, AB2 = AO2 + BO2 102 = AO2 + 82 100 = AO2 + 64 AO2 = 100 - 64 AO2 = 36 AO = 6 AC = 2 × AO = 2 × 6 = 12 cm Therefore, length of the other diagonal AC is 12 cm.

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