Sarah has two similar rectangular boxes. The dimensions of box 1 are four times those of box 2. How many times greater is the surface area of box 1 than the surface area of box 2?

The surface area of box 1 is 16 times greater than the surface area of box 2

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ---> the scale factor

In this problem the scale factor is equal to 4

so

step 2

How many times greater is the surface area of box 1 than the surface area of box 2?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

so

Let

z ----> the scale factor

x ----> surface area of box 1

y ---> surface area of box 2

so

we have

substitute

therefore

The surface area of box 1 is 16 times greater than the surface area of box 2