Respuesta :
Answer: 375
Step-by-step explanation:
If triangles ABC and DEF are similar, then their corresponding sides are proportional. Let's denote the ratio of corresponding sides of triangle DEF to triangle ABC as
�
k.
Given that the shortest side of triangle DEF is 75, and the shortest side of triangle ABC is 30, we can find the value of
�
k as follows:
�
=
shortest side of DEF
shortest side of ABC
=
75
30
=
5
2
k=
shortest side of ABC
shortest side of DEF
=
30
75
=
2
5
Now, since the sides of similar triangles are proportional, we can find the lengths of the other sides of triangle DEF:
Shortest side of DEF:
75
75
Shortest side of ABC:
30
30
Ratio
�
=
5
2
k=
2
5
So, the lengths of the sides of triangle DEF are:
Shortest side of DEF
=
75
Shortest side of DEF=75
Middle side of DEF
=
Middle side of ABC
×
�
=
40
×
5
2
=
100
Middle side of DEF=Middle side of ABC×k=40×
2
5
=100
Longest side of DEF
=
Longest side of ABC
×
�
=
80
×
5
2
=
200
Longest side of DEF=Longest side of ABC×k=80×
2
5
=200
Now, we can find the perimeter of triangle DEF by adding up the lengths of its sides:
Perimeter of DEF
=
75
+
100
+
200
=
375
Perimeter of DEF=75+100+200=375
So, the perimeter of triangle DEF is 375.
