Suppose the perimeter of a polygon is 27 inches. If the sides of the polygon are scaled by a factor of 1/3, what is the new perimeter?
Isn't the perimeter the sum of all the sides ?
Aren't the new sides 1/3 of the originals ?
Well ???
jane is making a building . how many croners does each combination of figures have
To find the new perimeter of a polygon when the sides are scaled by a factor of 1/3, follow these steps:
1. Start with the original perimeter: 27 inches.
2. Calculate the scaling factor: 1/3.
3. Multiply each side of the original polygon by the scaling factor.
4. Add up the lengths of the new scaled sides.
5. The result is the new perimeter.
Let's go through the calculations:
1. Original perimeter: 27 inches.
2. Scaling factor: 1/3.
3. Multiply each side length by the scaling factor:
Original side length * Scaling factor = New side length
4. Add up the lengths of the new scaled sides to find the new perimeter:
New perimeter = Sum of new side lengths
Let's apply this to the given question:
1. Original perimeter: 27 inches.
2. Scaling factor: 1/3.
To find the new perimeter, we need to multiply each side length of the original polygon by 1/3 and then add up the new side lengths.
Since we don't have the specific lengths of the sides in the original polygon, let's assume they are all the same length for simplicity. Let's call the length of each side "x".
Original side length = x
New side length = original side length * scaling factor = x * (1/3) = x/3
There are still x number of sides in the new polygon, so we need to add up x/3 a total of x times.
Sum of new side lengths = (x/3) + (x/3) + (x/3) + ... + (x/3) {x times}
Using the fact that there are x terms in the sum, we can write this as:
Sum of new side lengths = (x/3) * x
Simplifying further:
Sum of new side lengths = x^2/3
Therefore, the new perimeter is x^2/3.
Since we don't have the specific length of each side, we can't calculate the exact new perimeter. However, we know that it will be x^2/3, where "x" represents the original length of each side.