Final answer:
The area of the larger deck is 480 square feet, which is four times the area of the smaller deck with an area of 120 square feet. This increase is due to the scale factor of 2 applied to both the length and the width, causing the area to increase by a factor of 2 squared, or 4.
Step-by-step explanation:
Calculating the Area of Similar Rectangles
To solve the problem of finding the area of the larger deck, we need to understand the relationship of the areas of similar rectangles when the lengths are scaled. Since the length of the larger deck is twice the length of the smaller deck, we have a scale factor of 2. This scale factor applies to both the length and the width of the rectangle, as similar figures maintain their proportionality in all dimensions.
The area of the smaller deck is given as 120 square feet. When applying the scale factor of 2 to both the length and the width, the dimensions of the larger deck will be twice as long and twice as wide. However, the area of a rectangle is calculated by multiplying the length by the width. Therefore, if both dimensions are doubled, the area increases by a factor of 2 squared, which is 4. Hence, the area of the larger deck is 120 square feet multiplied by 4, resulting in 480 square feet.
To give a similar example, consider a square with a side length of 4 inches. If another square has a side length that is twice as long, the side length of the larger square would be 8 inches. The area of the larger square would then be 8 inches times 8 inches, which is 64 square inches. This is 4 times larger than the area of the smaller square, which is 16 square inches (4 inches times 4 inches). Remember, the ratio of the areas of similar figures is the square of the scale factor.