The scale factor for two similar retangles is 3. If the area of the smaller rectangle is 8m^2, what is the area of the larger rectangle.
if the scale factor is 3, the areas scale by 3^2 = 9
so, the larger area is 8*9 = 72m^2
To find the area of the larger rectangle, you can use the concept of scale factor. The scale factor between two similar figures is the ratio of their corresponding side lengths.
In this case, the scale factor is given as 3, which means that every side length of the larger rectangle is 3 times the corresponding side length of the smaller rectangle.
Since the scale factor applies to the side lengths, it also applies to the area of the rectangle. To find the area of the larger rectangle, you need to square the scale factor and multiply it by the area of the smaller rectangle.
Let's go step by step:
Step 1: Find the square of the scale factor:
Scale factor = 3
Scale factor squared = 3^2 = 9
Step 2: Multiply the square of the scale factor by the area of the smaller rectangle to find the area of the larger rectangle:
Area of larger rectangle = Scale factor squared * Area of smaller rectangle
Area of larger rectangle = 9 * 8 m^2
Area of larger rectangle = 72 m^2
So, the area of the larger rectangle is 72 square meters.