Question

A triangle with a perimeter of 19 units is dilated by a scale factor of ?. Find the 3/2 perimeter of the triangle after dilation. Round your answer to the nearest tenth, if necessary.

Answer 1

The scale factor of the dilation is
`\( (3)/(4) \),` and the 3/2 perimeter of the triangle after dilation is 28.5 units.

Step-by-step explanation:

A dilation involves resizing a figure by a certain scale factor. In this case, the perimeter of the original triangle is 19 units. The scale factor (denoted as
`\( k \))` can be found by dividing the perimeter of the dilated triangle
`(\( P' \))` by the original perimeter
`(\( P \))`:

`\[ k = (P')/(P) \]`

In this scenario, we are given that the original triangle has a perimeter of 19 units, so
`\( P = 19 \)`. The scale factor
`(\( k \))` is not explicitly given in the question, but it can be inferred that the dilated triangle's perimeter is
`\( (3)/(2) \)` times the original perimeter:

`\[ P' = (3)/(2) * P \]`

Substituting the given values:

`\[ P' = (3)/(2) * 19 \]`

`\[ P' = 28.5 \]`

Therefore, the dilated triangle's perimeter is 28.5 units. To find the scale factor
`(\( k \))`, we can use the formula mentioned earlier:

`\[ k = (P')/(P) \]`

Substituting the values:

`\[ k = (28.5)/(19) = (3)/(2) \]`

This confirms that the scale factor of the dilation is
`\( (3)/(2) \)`. So, the final answer is that the triangle is dilated by a scale factor of
`\( (3)/(2) \)`, and the 3/2 perimeter after dilation is 28.5 units.