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.

Answer 1

Given : Diagonals of rhombus interest at $0$.

$AB=10cm$ and $BD=16cm$

To find : Length of AC.

Solution:

Since, the diagonals of a rhombus bisect each other.

$\therefore OD=OB=\frac{16}{2}=8cm$

All sides of rhombus are equal.

$\therefore AB=BC=CD=DA=10cm$

In right angled triangle COD,

$(CD{)}^2=(OD{)}^2+(OC{)}^2$

or $\left(OC{)}^2\right(10{)}^2-(8{)}^2$

or, $OC=\sqrt{100-64}$

or, $OC=\sqrt{36}$

$\therefore OC=6cm$ $\therefore AC=12cm$

Hence the length of diagonal AC is 12 cm