Question

a square and an equilateral triangle have equal perimeters.If a diagnol of the square is 24 root 2 then find the area of the triangle​

Answer 1

Answer:

We know that,

perimeter of square= 4× side

And perimeter of equilateral triangle= p=3a

Given that,

square is 24 root 2

Then, Area of The triangle= 1/2 Base×height.

Answer 2

Answer:

It is given that the perimeters of a square and an equilateral triangles is same. And the length of the diagonal is given to us.

GiveN:

Length of the diagonal = 24√2

And we have to find the area of the triangle.....?

So, we know that the sides of the square are equal and the diagonal and two sides form a right angled triangle.

Let, the side of the square be a

By Pythagoras theoram,

➝ a² + a² = (24√2)²

➝ 2a² = 576 × 2

➝ a² = 576

➝ a = √576 = 24 cm

ATQ,

Perimeter of square = Perimeter of ∆

➝ 4 × side of square = 3 × side of triangle

➝ 4 × 24 cm = 3 × side of triangle

➝ Side of triangle = 4 × 24 / 3 cm

➝ Side of triangle = 32 cm

Now finding the area of the equilateral triangle,

Area of triangle = √3 / 4 × (side)²

➝ Area of the triangle = √3 / 4 × 32 × 32 cm²

➝ Area of the triangle = 256√3 cm²

So, the required area of the eq. triangle:

$\large{ \therefore{ \boxed{ \bf{ \red{256 \sqrt{3} {cm}^{2} }}}}}$

And we are done !!

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