A wire when bent in the form of an equilateral triangle encloses an area of cm². Find the area enclosed by the same wire when bent to form: (i) a square, and (ii) a rectangle whose length is 2 cm more than its width.

Question

KnowledgeBoat · Accepted Answer

Given, Area of equilateral triangle = cm² Consider x cm as the side of equilateral triangle We know that, Area of an equilateral triangle = Substituting the values we get, By formula, Perimeter of equilateral triangle = 3 × side = 3 × 12 = 36 cm. (i) As the same wire is now bent to form a square. ∴ Perimeter of equilateral triangle = Perimeter of square 36 = 4 × side Side = = 9 cm. Area of square = side × side = 9 × 9 = 81 cm². Hence, area enclosed by wire in form of square = 81 cm². (ii) As the same wire is now bent to form a rectangle. ∴ Perimeter of triangle = Perimeter of rectangle ........(1) According to the condition given for rectangle, Length is 2 cm more than its width Let width of rectangle = x cm ∴ Length of rectangle = (x + 2) cm Perimeter of rectangle = 2(l + b) Substituting the values in equation 1 we get, ⇒ 36 = 2[(x + 2) + x] ⇒ 36 = 2[2x + 2] ⇒ 4x + 4 = 36 ⇒ 4x = 32 ⇒ x = 8 cm. ∴ Length of rectangle = x + 2 = 8 + 2 = 10 cm and Breadth of rectangle = x = 8 cm. By formula, Area of rectangle = length × breadth = 10 × 8 = 80 cm². Hence, area enclosed by wire in form of square = 80 cm².

Mathematics

A wire when bent in the form of an equilateral triangle encloses an area of cm<sup>2</sup>. Find the area enclosed by the same wire when bent to form: (i) a square, and (ii) a rectangle whose length is 2 cm more than its width.

Mensuration

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