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Question
Prove that the ratio of the perimeters of two similar triangle is the same as the ratio if their corresponding sides.
Medium
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Solution
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Let
X
Y
Z
and
R
S
T
be two similar triangle
then
R
S
X
Y
=
R
T
X
Z
=
S
T
Y
Z
−
−
−
(
1
)
The perimeter of
△
X
Y
Z
=
X
Y
+
Y
Z
+
X
Z
−
−
−
(
2
)
The perimeter of
△
R
S
T
=
R
S
+
S
T
+
R
T
−
−
−
(
3
)
from equation
(
1
)
R
S
X
Y
=
R
T
X
Z
=
S
T
Y
Z
=
R
S
+
R
T
+
S
T
X
Y
+
X
Z
+
Y
Z
=
P
e
r
i
m
e
t
e
r
o
f
△
R
S
T
P
e
r
i
m
e
t
e
r
o
f
△
X
Y
Z
from
(
2
)
&
(
3
)
∴
Hence proved.
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