Question

ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, then find the length of other diagonal AC.

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Answer 1

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Answer 2

Given:-

Rhombus ABCD where AB = 10cm and BD = 16cm

To find:-

Length of the another diagonal AC.

Solution:-

A we can see that,

ΔAOB is a right angled triangle right angle at O                                                                                      

$OB=\frac{1}{2}BD$ and $OA=\frac{1}{2} AC$                                      

∴ $OB=\frac{1}{2}$×16 = 8CM                                                          

In ΔAOB, by PGT,

$AB^{2}=OA^{2} +OB^{2}$

⇒$10^{2} =OA^{2} +8^{2}$

⇒$OA^{2} =100-64=36$

∴$OA =\sqrt{36} =6cm$

∴AC = 2×OA = 2×6 = 12

Hence, OA = 12cm

Explanation:-

We know that diagonals of a rhombus bisect each other perpendicularly, that is why ∠AOB = 90°