Question 1127404

To find the area of a rhombus use:

{{{A=(1/2)d[1]*d[2]}}}

if the sides of a rhombus is {{{x}}}, the area of a square is {{{A=x^2}}}

if  the area of a rhombus equal to  {{{1/2}}}  the area of a square, we have

{{{((1/2)d[1]*d[2])/2=x^2}}}

{{{(1/4)d[1]*d[2]=x^2}}}

{{{d[1]*d[2]=4x^2}}}


Using Pythagoras: triangle formed bu side and half of diagonals

{{{(d[1]/2)^2+(d[2]/2)^2=x^2}}}

{{{d[1]^2/4+d[2]^2/4=x^2}}}

{{{d[1]^2+d[2]^2=4x^2}}}.......(2)

Hence the direct relation between diagonals are not possible.

Properties of Rhombus