A rectangle has length 8 cm by with 12 cm a similar rectangle has an area of 864 cm squared determine the length scale factor of the big rectangle to the smaller one?

To find the length scale factor, we first need to calculate the area of the smaller rectangle.

Area of the smaller rectangle = length x width
Area = 8 cm x 12 cm
Area = 96 cm²

Now, we can find the length scale factor by dividing the area of the larger rectangle by the area of the smaller rectangle:

Length scale factor = Area of larger rectangle / Area of smaller rectangle
Length scale factor = 864 cm² / 96 cm²
Length scale factor = 9

Therefore, the length scale factor of the larger rectangle to the smaller one is 9.

Step 1: Calculate the area of the smaller rectangle.

Area = length × width = 8 cm × 12 cm = 96 cm²

Step 2: Calculate the scale factor for the area.

Scale factor for area = Area of big rectangle / Area of small rectangle
Scale factor for area = 864 cm² / 96 cm²
Scale factor for area = 9

Step 3: Calculate the length scale factor.

Since the rectangles are similar, the length scale factor is the square root of the scale factor for area.

Length scale factor = √(Scale factor for area)
Length scale factor = √9
Length scale factor = 3

Therefore, the length scale factor of the big rectangle to the smaller one is 3.