I'm having trouble explaining this. See attachment. Can someone help ?
I'll call the first rectangle 'A' and the second 'B'.
For A, the perimeter is
$\displaystyle P_A=2w+2(2w+4)$
And for B:
$\displaystyle P_B=2(w+3)+2(3w-5)$
Do you see why that is? If so, then just plug in $\displaystyle w=5$, and see which perimeter is larger. To find out if there is a $\displaystyle w$ that would make the perimeters equal, just set $\displaystyle P_A=P_B$ and solve for $\displaystyle w$.
Thanks for the quick reply. I can solve for the perimeters of both rectangles but my problem is that this comes from my fourth-graders homework and I don't think they're actually trying to solve for the value of "w" but want the theory behind why they could or couldn't be equal. Could you please explain this ?