Answer:
The ratio of the area of triangle XBY to the area of triangle ABC is [tex]\frac{9}{25}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its areas is equal to the scale factor squared
In this problem
Triangles XBY and ABC are similar, because the corresponding internal angles are congruent
see the attached figure to better understand the problem
step 1
Find the scale factor
Let
z-------> the scale factor
[tex]z=\frac{BY}{BC}[/tex]
we have
[tex]BY=3\ units[/tex]
[tex]BC=2+3=5\ units[/tex]
substitute
[tex]z=\frac{3}{5}[/tex]
step 2
Find the ratio of the area of triangle XBY to the area of triangle ABC
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
we have
[tex]z=\frac{3}{5}[/tex] -----> scale factor
so
[tex]z^{2} =(\frac{3}{5})^{2} =\frac{9}{25}[/tex]
