Question

A square and an equilateral triangle have the same perimeter. The diagonal of the square is 9√2 cm. Find the area of the triangle.

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Answer 1

Answer:

Required answer is

$36 \sqrt{3}$

cm2

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Answer 2

Answer:

36√3 sq cm

Step-by-step explanation:

Diagonal of the square = 9√2 cm

=> Side of the square = 9cm

(Diagonal and two adjacent sides of a square makes a 90-45-45 triangle where the diagonal is the hypotenuse. Using Pythagorean theorem, we get:

(diagonal)² = (side)² + (side)²

2(side)² = (diagonal)²

=> side = diagonal/√2

Perimeter of square = 4*9 cm = 36 cm

Perimeter of square = Perimeter of equilateral triangle

=> Perimeter of equilateral Δ = 36 cm

=> Side of equilateral Δ = 12 cm

Using Heron's formula for equilateral triangle:

Area = √S(S - side)³

where S = half-perimeter = 18

Area of equilateral Δ = √18(18 - 12)³ = √(18*216) = √(1296*3) = 36√3

Area of equilateral triangle = 36√3 sq cm.