Question

22. Prove the area d' an equilateral mange described on one side d a square is
equal to the area of the sou lateral triangle described on one of its
ਨs​

Answer 1

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>>Prove that the area of an equilateral tr

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Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Medium

Solution

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Given:

ABCD is a Square,

DB is a diagonal of square,

△DEB and △CBF are Equilateral Triangles.

To Prove:

A(△DEB)

A(△CBF)

=

2

1

Proof:

Since, △DEB and △CBF are Equilateral Triangles.

∴ Their corresponding sides are in equal ratios.

In a Square ABCD, DB=BC

2

.....(1)

∴

A(△DEB)

A(△CBF)

=

4

3

×(DB)

2

4

3

×(BC)

2

∴

A(△DEB)

A(△CBF)

=

4

3

×(BC

2

)

2

4

3

×(BC)

2

(From 1)

∴

A(△DEB)

A(△CBF)

=

2

1