justin is using 120 inches of wire to biuld two structures one rectangle that is five times as long as it it is wide and one square whose si

justin is using 120 inches of wire to biuld two structures one rectangle that is five times as long as it it is wide and one square whose side lenght is the same as the width of the rectangle. what will be the exact area of his square?

So ......the perimeter of the rectangle is given by 2(L + W)= 2(5W + W) = 2(6W) = 12W

And the perimeter of the square is given by 4W

So

12W + 4W = 120

16W = 120

W = 7.5 inches

So...the area of the square is just   (7.5)^2 =  56.25 in²

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.

$$Area = W^2$$

$$Area = (7.5 inches)^2$$

$$Area = 56.25 inches^2$$