Question

Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to original) of the perimeters? the areas?

The ratio of the perimeters is ___.

The ratio of the areas is ___.

Answer 1

Part a) The ratio of the perimeters is 3

Part b) The ratio of the areas is 9

Answer 2

Part a) The ratio of the perimeters is
`3`

Part b) The ratio of the areas is
`9`

Explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

`z=(x)/(y)`

we have

`z=3`

substitute

`(x)/(y)=3`

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

`z^(2)=(x)/(y)`

we have

`z=3`

substitute

`(x)/(y)=3^(2)`

`(x)/(y)=9}`