the sides of a polygon are 8, 9, 29, 24, and 14 centimeters long. findd the length of the longest side similar polygon whose shortest side is 2.

The corresponding sides of a regular polygon are in the same ratio, so

8/2 = 29/x
8x = 58
x = 58/8 = 29/4

To find the length of the longest side of a similar polygon, where the shortest side is 2 units long, we can use the concept of ratios.

Given that the original polygon has sides of lengths 8, 9, 29, 24, and 14 centimeters, we can first determine the ratio between the sides of the original polygon and the similar polygon.

Since we want to find the longest side of the similar polygon, we need to find the scale factor between the shortest side of the original polygon (2 units) and the longest side of the original polygon. The longest side in the original polygon is 29 units long.

The scale factor is determined by dividing the longest side of the original polygon by the shortest side of the original polygon:
Scale factor = Longest side of original polygon / Shortest side of original polygon
= 29 cm / 2 cm
= 14.5

Now that we know the scale factor, we can apply it to the shortest side of the similar polygon (2 units) to find the length of the longest side:
Length of longest side of similar polygon = Scale factor * Shortest side of similar polygon
= 14.5 * 2 cm
= 29 cm

Therefore, the length of the longest side of the similar polygon is 29 centimeters.