1.

7. Prove that the area of an equilateral triangle described on one side of a squareto half the area of the equilateral triangle described on one of its diagonals.​

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Answer:

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ANSWER

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


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