Two similar figures have a scale factor of 5:6. The perimeter of the smaller figure is 25 inches. What is the perimeter of the larger figure?
(6/5) 25 = 30
5:6 = 25:30
To find the perimeter of the larger figure, we need to determine the scale factor between the two figures and use it to scale up the perimeter of the smaller figure.
Given that the scale factor is 5:6, we can express it as a fraction: 5/6. This means that every linear measurement on the smaller figure corresponds to 5/6 of that measurement on the larger figure.
Since the perimeter is the sum of all the sides of a figure, we can multiply each side length of the smaller figure by the scale factor to find the corresponding length on the larger figure.
Let's calculate it step by step:
1. Find the length of each side of the larger figure:
- Multiply the length of each side of the smaller figure by 5/6.
So, if the perimeter of the smaller figure is 25 inches, we can find the length of each side by dividing 25 by the number of sides. However, since we don't know the number of sides, let's assume it's a regular polygon with n sides:
Length of each side of the smaller figure = 25/n inches.
Now, multiply this length by 5/6:
Length of each side of the larger figure = (25/n) * (5/6) inches.
2. Calculate the total length of all sides of the larger figure:
- Multiply the length of each side of the larger figure by the number of sides (n).
Perimeter of the larger figure = n * [(25/n) * (5/6)] inches.
The n values cancel out, and the formula simplifies to:
Perimeter of the larger figure = 25 * (5/6) inches.
Now, we can calculate the perimeter of the larger figure:
Perimeter of the larger figure = 25 * (5/6)
= 125/6 inches.
The perimeter of the larger figure is 125/6 inches, or approximately 20.83 inches.