Final answer:
To find the dimensions of the rectangle, set up and solve an equation. The width is approximately 3.43 inches and the length is approximately 20.57 inches. The area of the rectangle is approximately 70.58 square inches.
Step-by-step explanation:
To find the dimensions of the rectangle, we can set up an equation using the information given. Let's say the width of the rectangle is x inches. According to the problem, the length is six times the width, so the length would be 6x inches. The perimeter of a rectangle is given by the formula P = 2(length + width), so we can set up the equation 48 = 2(6x + x) and solve for x.
Simplifying the equation, we get 48 = 2(7x), which can be further simplified to 48 = 14x. Dividing both sides by 14, we find that x = 48/14 = 3.43 inches. Therefore, the width of the rectangle is approximately 3.43 inches and the length is approximately 6(3.43) = 20.57 inches.
To find the area of the rectangle, we can use the formula A = length * width. Substituting the values we found, we get A = 3.43 * 20.57 = 70.58 square inches.