Question

A square and an equilateral triangle have equal perimeters.If a diagonal of the square is 24√2,then find the area of the triangle

Answer 1

256√3 unit^2

Step-by-step explanation:

We know, for a square of side a, length of diagonal is a√2.

So, let the side of this square be 'a'.

=> a√2 = length of diagonal

=> a√2 = 24√2

=> a = 24, it means that the length of square is 24.

Since triangle & square have same perimeter,

=> perimeter of square = perimeter of triangle

=> 4a = 3* side of ∆

=> 4(24) = 3 * side of ∆

=> 4(24/3) = side of ∆

=> 32 = side of ∆

As, we know, area of equilateral ∆ is √3/4 side². Thus,

Area of ∆ = √3/4 *32² = 256√3 unit²

Answer 2

hey buddy here is your answer

Let the side of the square is X

Diagonal of square=X√2

ATQ,

     X√2=24√2

  =>X=24

then side of the square = 24 units

then area of the square= 96 units

It is given that perimeter of the equilateral triangle= perimeter of square

hence area of equilateral triangle = 96 units

then each side of the triangle = 96/3 = 32 units

Hence area of the equilateral triangle = (√3/4)(32*32)

                                                                 = 256√3 units^2

Hope it helps

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