Question

In a rhombus of side 10 cm, one of the diagonals is 12 m long. Find the length of the second diagonal.

Answer 1

Let ABCD be the given rhombus whose diagonals intersect at O. Then,

$AB=10cm$

Let $AC=12cm$ and $BD=2xcm$

We know that the diagonals of a rhombus bisect each other at right angle.

Therefore,

$OA=\frac{1}{2}AC=6cm$

$OB=\frac{1}{2}BD=xcm$

$\angle AOB={90}^o$

In right triangle $△AOB$,

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

$(10{)}^2=x^2+6^2$

$x^2=64$

$x=8cm$

Therefore, length of second diagonal = $2x=16cm$