Step one: We need to find the formula for perimeter. And we can't just say "count all the sides". How can we express it? It's length + length + width + width, right? Let's size that down a little bit. 2*length 2*width. We'll use w to express "width" and 2w to express "length".
2(w)+2(2w)=48.
6w=48.
w=8.
Since length is twice the width, 8*2 is 16. Length=16.
You can check it by substituting the different values for length and width into the equation 2w+2l=perimeter.
2(8)+2(16)=48. Is this true? Yep! So you know you're right.