The shortest side of two polygons have lenghts in the ratio 2:5.The perimeter of the smallest polygon is 20. what is the perimeter of the large polygon?
This can only be answered if the two polygons are similar, so I will assume they are
then if P is the perimeter of the larger
P/20 = 5/2
P = (5/2)(20) = 50
To find the perimeter of the larger polygon, we need to determine the ratio of the perimeters based on the given ratio of the lengths of the shortest side of the two polygons.
Let's assume the shortest side of the smaller polygon is represented by 2x, where x is the common ratio. Therefore, the perimeter of the smaller polygon can be found using the formula:
Perimeter of smaller polygon = 20
Now, we know that the ratio of the lengths of the shortest side of the two polygons is 2:5. So, the shortest side of the larger polygon can be represented by 5x.
To find the perimeter of the larger polygon, we can use proportions. The ratio of perimeters is the same as the ratio of corresponding side lengths, so we have:
Perimeter of larger polygon / 20 = (5x) / (2x)
Cross-multiplying the equation gives us:
Perimeter of larger polygon = (5x / 2x) * 20
Simplifying further:
Perimeter of larger polygon = (5/2) * 20
Perimeter of larger polygon = 50
Therefore, the perimeter of the larger polygon is 50 units.