The formula for the perimeter of a rectangle is 2l +2w, where l = length and w= width. That gives us the first equation: 212 = 2l + 2w
If the length is 16 more than 5 times the width then: l = 5w + 16
Now we replace (substitute) the l from the first equation with the 5w +16 from the second, since that tells us they are identical.
That gives us: 212 = 2(5w + 16) + 2w
Now we can solve for w...
212 = 2(5w +16) + 2w
212 = 10w + 32 + 2w
212 = 12w + 32
180 = 12w
15 = w
Now we use the second equation an solve for l...
l = 5w + 16
l = 5(15) + 16
l = 75 + 16
l = 91
Now plug both l and w into the original perimeter formula to verify...
212 = 2l + 2w
212 = 2(91) + 2(15)
212 = 182 + 30
212 = 212
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