Question 1013431

all sides of a rhombus are equal in length.
the diagonals of the rhombus intersect at a {{{90}}} degree angle.
the diagonals and the sides of the rhombus form four right triangles whose sides are:
one leg of these right triangles is equal to {{{(1/2)}}}  the  length  of the one diagonal
the other leg of these right triangles is equal to {{{(1/2)}}}  the  length  of the other diagonal
the hypothenuse is equal to the length of the side we are looking for

so, if side is {{{a}}}, use Pythagoras theorem to find it using the length of the legs

one leg is {{{(1/2)12cm=6cm}}} long and the other leg is {{{(1/2)19cm=4.5cm}}} long

then 
{{{a^2=(6cm)^2+(4.5cm)^2}}}
{{{a^2=36cm^2+20.25cm^2}}}
{{{a^2=56.25cm^2}}}
{{{a=sqrt(56.25cm^2)}}}
{{{a=7.5cm}}}