A rectangle has dimensions 4 ft by 6 ft. Show that if the length and width are doubled, the area is 4 times as large.
hey
ANY 2 dimensional figure if its scale is multiplied by x its AREA is multiplied by x^2
2^2 = 4
or in this case 2L * 2 w = 4 L w
4 * 6 = 24 square feet
8 * 12 = 96 square feet
96 / 24 = 4
freereerer
To demonstrate that doubling both the length and width of a rectangle results in an area four times as large, you can compare the areas of the original and resized rectangles.
First, let's calculate the area of the original rectangle with dimensions 4 ft by 6 ft. The formula for the area of a rectangle is given by length multiplied by width:
Area = length × width
= 4 ft × 6 ft
= 24 square feet
Now, let's double both the length and width of the rectangle. The new dimensions will be 4 ft × 2 = 8 ft for the length and 6 ft × 2 = 12 ft for the width.
Next, we calculate the area of the resized rectangle using the same formula:
Area (resized) = length × width
= 8 ft × 12 ft
= 96 square feet
To compare the areas, we divide the area of the resized rectangle by the area of the original rectangle:
96 square feet / 24 square feet = 4
As a result, the area of the resized rectangle is four times as large as the original rectangle. This supports the claim that if the length and width are doubled, the area will also be four times as large.