The sides of a triangle are times the sides of another triangle. Find the scale factor of their perimeters.
Answers
Answered by
2
Answer:
Scale factors of triangle =a:b
Let the triangles be △ABC and △DEF
Given
DE
AB
=
EF
BC
=
DF
AC
=
b
a
⇒AB=
b
a
DE,BC=
b
a
EF,AC=
b
a
DF
Perimeter(△DEF)
Perimeter(△ABC)
=
DE+EF+DF
AB+BC+AC
⇒
Perimeter(△DEF)
Perimeter(△ABC)
=
DE+EF+DF
b
a
DE+
b
a
EF+
b
a
DF
⇒
Perimeter(△DEF)
Perimeter(△ABC)
=
b
a
(
DE+EF+DF
DE+EF+DF
)=
b
a
Answered by
17
Step-by-step explanation:
this is very simple question
Scale factors of triangle =a:b
Let the triangles be △ABC and △DEF
Given
DE
AB
=
EF
BC
=
DF
AC
=
b
a
⇒AB=
b
a
DE,BC=
b
a
EF,AC=
b
a
DF
Perimeter(△DEF)
Perimeter(△ABC)
=
DE+EF+DF
AB+BC+AC
⇒
Perimeter(△DEF)
Perimeter(△ABC)
=
DE+EF+DF
b
a
DE+
b
a
EF+
b
a
DF
⇒
Perimeter(△DEF)
Perimeter(△ABC)
=
b
a
(
DE+EF+DF
DE+EF+DF
)=
b
a
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