Triangle ABC ~ triangle XYZ, AB=12,XY=30, BC = 10, If perimeter of triangle ABC =40cm then what is the perimeter of triangle XYZ?
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Step-by-step explanation:
Let △ABC and △DEF be two similar triangles of perimeters P
1
and P
2
respectively.
Also, let AB=12 cm, P
1
=30 cm and P
2
=20 cm.
Then,
DE
AB
=
EF
BC
=
DF
AC
=
P
2
P
1
[∵ Ration of corresponding sides of similar triangles is equal to the ratio of their perimeters]
⇒
DE
AB
=
P
2
P
1
⇒
DE
12
=
20
30
⇒ DE=
30
12×20
cm=8cm
Hence, the corresponding side of the second triangle is 8 cm
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