Answer:
7. [tex]BC=22[/tex]
8. [tex]EF=8[/tex]
Step-by-step explanation:
7.
It is given that triangle (ABC) is similar to triangle (DEF). This means that triangle (DEF) is a scaled version of the triangle (ABC). Between these two triangles, there is a ratio. This ratio referred to as the ratio of similitude, is a factor that one multiplies a side of the triangle by, to get the length of the corresponding side in the other triangle. This number can be found by dividing the corresponding sides in the triangle.
As per the given picture, side (AB) corresponds to side (DE). Therefore divide side (AB) by (DE) to find the ratio of similitude,
[tex]\frac{AB}{DE}=\frac{10}{5}=2[/tex]
Multiply side (EF) by the ratio of similitude to find the length of its corresponding side (BC).
[tex]2(EF) = 2(11) = 22[/tex]
[tex]BC=22[/tex]
8.
The triangles (ABC) and (DEF) are similar. One can use the same logic applied to the last problem to solve this problem. For further reference, read the intro written to explain the process used to solve the problem (7).
One can see that sides (AB) and (DE) are corresponding sides, divide (DE) by (AB) to find the ratio of similitude;
[tex]\frac{DE}{AB}=\frac{4}{6}=\frac{2}{3}[/tex]
Now multiply this number by side (BC) to find the length of the corresponding side (EF);
[tex](BC)*\frac{2}{3}=EF\\12*\frac{2}{3}=EF\\8=EF[/tex]
