Question

If ABCD is a rhombus, prove that
$4 {ab}^{2} = {ac}^{2} + {bd}^{2}$

Answer 1

hay!!

Dear user -

in given ABCD rhombus 4ab²
Than prove that ac²+bd²

we use this figure

so,

OA=1/2AC,OB=1/2BD
and △ AOB=90

in Right △AOB, using the above theorem

AB²=OA²+OB²

=> (1/2AC)²+(1/2BD)²

=> AC²+BD²
so,

Hence 4ab²=ac²+bd²

I hope it's help you