Math, asked by govinda2863, 1 day ago

AD is an altitude of an equilateral triangle ABC. On AD as base another equilateral triangle ADE is constructed. Prove that ar(∆MDE): ar(∆ABC)

Answers

Answered by rishisinghparihar
0

Step-by-step explanation:

We have an equilateral △ABC in which AD is altitude. An equilateral △ADE is drawn using AD as base.

Since, the two triangle are equilateral, the two triangles will be similar also.

△ADE∼△ABC

We know that according to the theorem, the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

ar(△ABC)

ar(△ADE)

=(

AB

AD

)

2

----- ( 1 )

Now, △ABC is an equilateral triangle.

∴ ∠B=60

o

⇒ sinB=

AB

AD

⇒ sin60

o

=

AB

AD

2

3

=

AB

AD

⇒ (

AB

AD

)

2

=

4

3

Substituting above value in equation ( 1 ) we get,

ar(△ABC)

ar(△ADE)

=

4

3

------ Hence proved

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