Answer:
40cm
Step-by-step explanation:
Since the pentagons are similar, the corresponding sides are in the same ratio.
[tex]\dfrac{4x}{48}=\dfrac{x}{x+2} \\\text{Cross Multiply}\\4x(x+2)=48x\\4x^2+8x=48x=0\\4x^2=48x-8x\\4x^2=40x\\4x=40\\x=10\:cm[/tex]
The width of the badge = 4x
=4 X 10
=40cm
The width of the badge is 40cm.