The perimeter of two similar triangles are 40 cm and 25 cm. If one altitude of former triangle is 24 cm, then the length of the corresponding altitude of the later triangle is
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Answer:
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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