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