The length of diagonal of a square is 9√2 cm. The square is reshaped to form a equilateral triangle in such a way that the perimeter remain… — Answer & Discussion

The length of diagonal of a square is 9√2 cm. The square is reshaped to form a equilateral triangle in such a way that the perimeter remains same. What is the area (in cm 2) of largest in circle that can be formed in that triangle?

A6π
B9π
C12π
D15π

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Discussion 1

CCommunity05 Jun 2019

Side of square is 9√2/√2 = 9 cm

Perimeter of Square = 4 × 9 = 36 cm

⇒ Side of equilateral triangle = perimeter/3

⇒ Side of equilateral triangle = 36/3

⇒ Side of equilateral triangle = 12 cm

Radius of largest incircle can be given as = side of equilateral triangle /2√3

⇒ Radius of largest incircle = 12/2√3 = 6/√3 cm

Area of circle is = πr2

⇒ Area = π × (6/√3)2 = 12π

∴ the area of in circle is 12π