Log explanation below; answer is at bottom.
If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,
p = 2l +2w,
is 7 x w, then
w = p/7
When two things are set equal to the same variable, they are equal to each other, so,
l - 12 = p/7
Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,
l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,
l - 12 = (2l + 2(l - 12))/7
To solve this you want to multiply both sides by 7 first to get rid of the fraction.
7l - 84 = 2l + 2(l - 12)
Next you want to distribute the 2 over the l and the 12.
7l - 84 = 2l + 2l - 24
Next you want to combine like terms on each side.
7l - 84 = 4l - 24
Next add 84 and subtract 4l from sides to isolate the variable.
3l = 60
Now divide each side by 11 to get your answer.
l = 20.
To find the width,
w = l - 12
Just plug in and solve.
w = 20 - 12
w = 8
So your length and width are 20 and 8.
l = 20
w = 8
