answer
width = 98 cm
length = 105 cm
set up equations
the perimeter of a rectangle = 2W + 2L
p = 2W + 2L
the perimeter is also 406
406 = 2W + 2L
we know that the length of the rectangle is 7 cm longer than the width so
L = W + 7
substitute equations and solve for width
plug L into p = 2W + 2L to get
406 = 2W + 2(W + 7) distribute the 2 to the terms in the parentheses
406 = 2W + 2W + 14
406 = 4W + 14
392 = 4W
W = 98
substitute equations and solve for length
now that we know the width, we can substitute W in L = W + 7 to find length
L = W + 7
L = 98 + 7
L = 105
final dimensions
width = 98 cm
length = 105 cm
