Question

prove that the area of an equitateral triangle described on one side of square is equal to half the area of the equilateral triangle described on one of its diagonal​

Answer 1

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

∴ A(△DEB)

A(△CBF)

= 43 ×(DB) 243 ×(BC) 2

∴ A(△DEB)

A(△CBF)

= 43 ×(BC 2 ) 2 43

×(BC) 2

∴ A(△DEB)

A(△CBF)

= 21

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