Question

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

Answer 1

Step-by-step explanation:

Given:

ABCD is a Square,

DB is a diagonal of square,

△DEB and △CBF are Equilateral Triangles.

To Prove:

A(△DEB)A(△CBF)=21

Proof:

Since, △DEB and △CBF are Equilateral triangles.

∴ Their corresponding sides are in equal ratios.

In a Square ABCD, DB=BC2 .....(1)

∴ A(△DEB)A(△CBF)=43×(DB)243×(BC)2

∴ A(△DEB)A(△CBF)=43×(BC2)243×(BC)2 (From 1)

 A(△DEB)A(△CBF)=21

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