the sides of a polygon are 3,4,5,6 and 7cm. Find the perimeter of a similar polygon, if the sides corresponding to 5cm is 9cm long.
5.4, 7.2, 9, 10.8 and 12.6 are the measurements of each side. The perimeter is 45.
multiply all the sides by 9/5
To find the perimeter of a similar polygon, we need to know the scale factor between the original polygon and the similar polygon.
First, let's find the scale factor by comparing the corresponding sides. The original polygon has sides 3, 4, 5, 6, and 7 cm long, while the similar polygon has a side corresponding to 5 cm that is 9 cm long.
The scale factor is the ratio of the corresponding sides, which in this case is 9 cm / 5 cm = 1.8.
To find the perimeter of the similar polygon, we multiply each side length of the original polygon by the scale factor.
Perimeter of the similar polygon = (3 cm + 4 cm + 5 cm + 6 cm + 7 cm) × 1.8
Perimeter of the similar polygon = 25 cm × 1.8
Perimeter of the similar polygon = 45 cm
Therefore, the perimeter of the similar polygon is 45 cm.
To find the perimeter of the similar polygon, we first need to determine the scale factor between the corresponding sides of the original and similar polygons.
The scale factor (k) can be found by dividing the length of the corresponding sides of the similar and original polygons. In this case, we divide the length of the corresponding sides of the similar polygon (9 cm) by the length of the corresponding sides of the original polygon (5 cm).
k = 9 cm / 5 cm
k = 1.8
Now, we can use this scale factor to determine the lengths of the corresponding sides of the original polygon, which will allow us to find its perimeter.
By multiplying each side length of the original polygon by the scale factor (k = 1.8), we get:
Side 1: 3 cm * 1.8 = 5.4 cm
Side 2: 4 cm * 1.8 = 7.2 cm
Side 3: 5 cm * 1.8 = 9 cm (corresponding side in the similar polygon)
Side 4: 6 cm * 1.8 = 10.8 cm
Side 5: 7 cm * 1.8 = 12.6 cm
Now, we can calculate the perimeter of the original polygon by adding up the lengths of all its sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4 + Side 5
Perimeter = 5.4 cm + 7.2 cm + 9 cm + 10.8 cm + 12.6 cm
Perimeter = 45 cm
Therefore, the perimeter of the similar polygon, when the corresponding side to 5 cm is 9 cm long, is 45 cm.