In the given figure, ABCD is a rhombus whose diagonals AC and BD intersect at a point O. If side AB =10 cm and diagonal BD =16 cm, find the length of diagonal AC.
Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM
Expert Answer:
We know that the diagonals of a rhombus bisect each other at right angles.
∴ BO =
BD = 
cm = 8 cm, AB =10 cm and ∠AOB = 900 .
From right triangle OAB, we have
AB2 = AO2 + BO2
⇒AO2 = (AB2 - BO2) = {(10)2 -(8)2} cm2
= (100 -64) cm2 = 36 cm2
⇒ AO = 
cm = 6 cm.
∴ AC = 2 × AO = (2×6) cm = 12 cm.
Answered by | 4th Jun, 2014, 03:23: PM
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