Answer:
48
Step-by-step explanation:
In similar polygons, every side of one polygon is a certain number of times bigger than the corresponding side of the other polygon. This number is the scale factor. Since the perimeter of each polygon is the sum of the lengths of the sides of that polygon, the perimeters also have the same scale factor that the sides do.
For example, if a triangle has 3 sides measuring 5 cm each and a similar triangle has 3 sides measuring 10 cm each, you see that each side of the second triangle is 2 times the length of the corresponding side of the first triangle. The scale factor from the smaller triangle to the larger triangle is 2. Now look at the perimeters. Since 5 + 5 + 5 = 15 and 10 + 10 + 10 = 30, the perimeters are 15 cm and 30 cm, and again, the perimeter of the second triangle is the same 2 times bigger than the perimeter of the first triangle.
Now look at your problem.
The perimeter of the smaller flag to the right is 16.
We see a side on the larger flag is 15, but we don't see the same side length on the smaller flag, so 15 does not help us.
Now we see that a side of the smaller flag measures 4 and the corresponding side of the larger flag measures 12. We divide the larger side length by the corresponding smaller side length to find the scale factor.
12/4 = 3
The scale factor from the smaller flag to the larger flag is 3. The perimeters also have the same scale factor of 3.
perimeter = 3 * 16 = 48
Answer: 48
