The sides of a rectangle are increased by a scale factor of 4. The perimeter of the smaller rectangle is 20cm. What is the perimeter of the larger rectangle?
320 cm
80 cm
120 cm
60 cm

2. A right triangle has an area of 24 ft squared. The dimensions of the triangle are increased by a scale factor of 6. What is the area of the new triangle?

48 ft squared
72 ft squared
144 ft squared
864 ft squared

The scale factor, also called the linear scale factor, is the proportion (ratio) between the length of the same side in two similar figures, that is, figures that have the same shape but different sizes.

A scale factor not only allows to relate the length of the same side, but also the dimensions of the figures such as the area or the perimeter while the figures are similar, as in these cases.

To obtain a measure of the larger figure and have the value of the smaller figure, this value is multiplied by the scale factor.

To obtain a measure of the smallest figure and have the value of the larger figure, said value is divided by the scale factor.

In the first case the perimeter of the smaller rectangle is 20cm. It is desired to obtain the perimeter of the largest rectangle, then knowing that the scale factor is 4, the perimeter of the smallest rectangle is multiplied by the scale factor (because it is desired to increase the size of the rectangle):

4*20cm= 80 cm

So, the perimeter of the larger rectangle is 80 cm.

Similarly in the second case, the area of the smallest triangle is 24 ft squared. It is desired to obtain the area of the new triangle, then knowing that the scale factor is 6, the area of the smallest triangle is multiplied by the scale factor (because it is desired to increase the size of the triangle):

6*24 ft squared= 144 ft squared

So, the area of the new triangle is 144 ft squared.