Answer:
Part a) The ratio of the perimeters is [tex]3[/tex]
Part b) The ratio of the areas is [tex]9[/tex]
Step-by-step 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
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=3[/tex]
substitute
[tex]\frac{x}{y}=3[/tex]
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
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=3[/tex]
substitute
[tex]\frac{x}{y}=3^{2}[/tex]
[tex]\frac{x}{y}=9}[/tex]
