Answer:
The areas of triangles are [tex]46.8\ cm^{2}[/tex] and [tex]83.2\ cm^{2}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its perimeters is equal to the scale factor
and
The ratio of its areas is equal to the scale factor squared
Let
z-------> the scale factor
x-----> the area of the larger triangle
y-----> the area of the smaller triangle
so
[tex]z^{2}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{4}{3}[/tex]
[tex](\frac{4}{3})^{2}=\frac{x}{y}[/tex]
[tex]x=\frac{16}{9}y[/tex] ------> equation A
[tex]x+y=130[/tex] ------> equation B
substitute equation A in equation B
[tex]\frac{16}{9}y+y=130[/tex]
[tex]\frac{25}{9}y=130[/tex]
[tex]y=130*9/25=46.8\ cm^{2}[/tex]
Find the value of x
[tex]x=\frac{16}{9}(46.8)=83.2\ cm^{2}[/tex]