A dilation scale factor 2 maps triangle RST to R'S'T'. The perimeter of triangle RST is 60. What is the perimeter of triangle R'S'T'?
since perimeter is a linear quantity, it scales the same as the length: the scale factor is 2.
To find the perimeter of triangle R'S'T', we need to understand how a dilation affects the sides of a triangle.
A dilation is a transformation that resizes a figure while maintaining the shape. The scale factor determines the amount by which the figure is enlarged or reduced. In this case, the dilation scale factor is 2, which means every length in triangle RST will be multiplied by 2 to get the corresponding length in triangle R'S'T'.
Since the perimeter of a polygon is the sum of the lengths of its sides, we can find the perimeter of triangle R'S'T' by multiplying the scale factor by each side length of triangle RST and then adding them up.
Let's assume the side lengths of triangle RST are a, b, and c. Then the side lengths of triangle R'S'T' can be found by multiplying each side length by 2, which gives us 2a, 2b, and 2c.
Therefore, the perimeter of triangle R'S'T' is (2a + 2b + 2c).
However, we don't have the actual side lengths of triangle RST, only its perimeter, which is 60. This means we need to make some assumptions about the side lengths.
If we assume that each side of triangle RST is equal in length, we can divide the perimeter by 3 to get the length of each side, which is 20.
Then, using the dilation scale factor of 2, we can find the side lengths of triangle R'S'T':
Side RS of triangle R'S'T' = 2 * 20 = 40
Side ST of triangle R'S'T' = 2 * 20 = 40
Side RT of triangle R'S'T' = 2 * 20 = 40
Now we can find the perimeter of triangle R'S'T' by adding up these side lengths:
Perimeter of R'S'T' = (40 + 40 + 40) = 120
Therefore, the perimeter of triangle R'S'T' is 120.