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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

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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

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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

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

## Answers ( )

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.

question

November 22, 2019

avatar

Debabrata Sevda

Share

Save

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……