Question 1125382


if pentagons are similar, corresponding sides are proportional; so, we have

{{{4x:48=x:(x+2)}}}.............solve for {{{x}}}

{{{4x(x+2)=48x}}} ...simplify
{{{cross(4)cross(x)(x+2)=cross(48)12cross(x)}}}
{{{(x+2)=12}}}
{{{x=12-2}}}
{{{x=10}}}

dimensions of greater pentagon are: 
{{{4x*cm=4*10cm=40cm}}} and {{{48cm}}}

dimensions of smaller pentagon are: 
{{{x=10}}} and {{{x+2=12}}}

I hope you can find out what the width of the badge is.