Question

prove that area of an equilateral triangle inscribed on one side of a square is equal to half the equilateral triangle inscrined on the diagonal of the same square​

Answer 1

Hey there!

Here is your answer

FIGURE IN THE ATTACHMENT

Let the sides of the square be x

BC=AB=AD=DC=X

Diagonal AC=√2x

Triangle AEC is similar to triangle BFC( Equilateral triangles)

Applying theorem 6.6

The ratio of the areas of two similar triangles is equal to the square of the ration of their corresponding sides.

(X)^2/(√2x)^2 = area(BFC)/area(AEC)

= X^2/2X^2

=1/2

Hence proved!()

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