Answer:
The area of triangle DEF is [tex]282\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
To find the scale factor, divide the height of triangle DEF by the height of triangle ABC
Let
z ------> the scale factor
[tex]z=\frac{13}{5}[/tex]
step 2
Find the area of triangle DEF
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 triangle DEF
y -----> the area of triangle ABC
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{13}{5}[/tex]
[tex]y=15\ cm^{2}[/tex]
substitute and solve for x
[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]
[tex]x=(\frac{169}{25})(15)[/tex]
[tex]x=282\ cm^{2}[/tex]
