The larger square has an area of 1,089 square feet and the smaller square has an area of 121 square inches. What is the scale factor between the two squares?
area grows as the square of the scale, so that makes the scale
√121 in : √1089 ft
= 11in : 33 ft
= 11in : 396in
= 1:36
To find the scale factor between the two squares, we need to compare their areas.
1 square foot is equal to 12 inches, so to convert the area of the larger square from square feet to square inches, we multiply by 12^2 (since the conversion is done on both length and width).
Area of the larger square in square inches = 1,089 square feet * (12 inches/foot)^2 = 1,089 * 144 = 156,816 square inches
Now, we can find the scale factor by dividing the area of the larger square by the area of the smaller square.
Scale factor = Area of larger square / Area of smaller square
= 156,816 square inches / 121 square inches
= 1,296
Therefore, the scale factor between the two squares is 1,296.
To find the scale factor between two squares, we need to compare their areas.
First, let's convert the area of the larger square from square feet to square inches to have a consistent unit for comparison. Since 1 square foot is equal to 144 square inches, we can multiply the area of the larger square by 144.
Area of larger square = 1,089 square feet * 144 square inches per square foot
Calculating this:
Area of larger square = 156,816 square inches.
Now, we can compare the areas of the two squares:
Scale factor = (Area of larger square) / (Area of smaller square)
Scale factor = 156,816 square inches / 121 square inches
Calculating this:
Scale factor = 1,296
Therefore, the scale factor between the two squares is 1,296.