Answer:
Part 1) The ratio of the areas of triangle TOS to triangle TQR is [tex]\frac{4}{25}[/tex]
Part 2) The ratio of the areas of triangle TOS to triangle QOP is [tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Part 1) Find the ratio of the areas of triangle TOS to triangle TQR
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/TR
substitute the values
6/(6+9)
6/15=2/5
step 2
Find the ratio of the areas of triangle TOS to triangle TQR
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{5})^{2}=\frac{4}{25}[/tex]
Part 2) Find the ratio of the areas of triangle TOS to triangle QOP
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/QP
substitute the values
6/9
6/9=2/3
step 2
Find the ratio of the areas of triangle TOS to triangle QOP
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{3})^{2}=\frac{4}{9}[/tex]
