The perimeter of a rectangle is two times its length (L) plus two times its width (W).
The perimeter of a square is four times its side (S).
The total perimeter (P) is: $$P = 2L + 2W + 4S$$
We also know that:
$$P = 120$$ (120 inches of wire)
$$L = 5W$$ (five times as long as it is wide)
$$S = W$$ (whose side lenght is the same as the width of the rectangle)
We get:
$$120 = 10W + 2W + 4W$$
$$120 = 16W$$
$$W = \frac{120}{16}$$
$$W = 7.5 inches$$
The area of the square is given by its side length squared (S²). Since $$S=W$$, the area of the square is W².
$$Area = W^2$$
$$Area = (7.5 inches)^2$$
$$Area = 56.25 inches^2$$
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