two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal
Please solve on Paper
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two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal
Please solve on Paper
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MATHS
In given figure two isosceles triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights.
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November 22, 2019
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Debabrata Sevda
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ANSWER
Let △ABC and △DEF be the given triangles such that AB=AC and DE=DF, ∠A=∠D
and
Area(△DEF)
Area(△ABC)
=
25
16
.......(i)
Draw AL⊥BC and DM⊥EF.
Now, AB=AC,DE=DF
⇒
AC
AB
=1 and
DF
DE
=1
⇒
AC
AB
=
DF
DE
⇒
DE
AB
=
DF
AC
Thus, in triangles ABC and DEF, we have
DE
AB
=
DF
AC
and ∠A=∠D [Given]
So, by SAS-similarity criterion, we have
△ABC∼△DEF
⇒
Area(△DEF)
Area(△ABC)
=
DM
2
AL
2
⇒
25
16
=
DM
2
AL
2
[Using (i)]
⇒
DM
AL
=
5
4
Hence, AL:DM=4:5.....
......i hope it's helpful for u......