Answer:
Part 1) The ratio of the perimeter of ΔHKO to the perimeter of ΔFGO is [tex]\frac{1}{2}[/tex]
Part 2) The ratio of the area of ΔKHO to the area of ΔGFO is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Part 1)
we know that
If two figures are similar , then the ratio of its perimeters is equal to the scale factor
In this problem
Triangles HKO and FGO are similar by AAA Theorem
Find the scale factor
The scale factor is equal to the ratio of its corresponding sides
[tex]\frac{4}{8}=\frac{7}{14}=\frac{1}{2}[/tex]
Part 2) Find the ratio of the area of ΔKHO to the area of ΔGFO
Area of ΔKHO
[tex]A=4*7/2=14\ units^{2}[/tex]
Area of ΔGFO
[tex]A=8*14/2=56\ units^{2}[/tex]
The ratio of its areas is equal to
[tex]\frac{14}{56}=\frac{1}{4}[/tex]
Alternative Method
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem we have that
The scale factor is [tex]\frac{1}{2}[/tex]
so
squared the scale factor
[tex](\frac{1}{2})^{2}=\frac{1}{4}[/tex] ----> is correct
