Question

The length of each side of a rhombus is 10 cm and one if its diagonals is of length 16 cm. The length of the other diagonal is
(a) 13 cm
(b) 12 cm
(c) $\frac{23}{9}$ cm
(d) 6 cm

Answer 1

Correct option is B.$12cm$

Let $ABCD$ be the rhombus such that $AB=BC=CD=AC=10cm$ and $BD=16cm$

Let the two diagonals intersect at $O$.

$\therefore DO=BO=\frac{16}{2}=8cm$ [Diagonals bisect each other at ${90}^{\circ }$]

Now, By Pythagoras Theorem, in $\Delta AOB$,

$\Rightarrow B{O}^2+A{O}^2=A{B}^2$

$\Rightarrow 8^2+A{O}^2={10}^2$

$\Rightarrow AO=\sqrt{100-64}$

$\therefore AO=6cm$

Hence, $AC=2\times AO=12cm$