A wire when bent in the form of a square encloses an area of 484 m². Find the largest area enclosed by the same wire when bent to form :
(i) an equilateral triangle.
(ii) a rectangle of breadth 16 m.

Question

A wire when bent in the form of a square encloses an area of 484 m². Find the largest area enclosed by the same wire when bent to form : (i) an equilateral triangle. (ii) a rectangle of breadth 16 m.

KnowledgeBoat · Accepted Answer

(i) Area of the square = 484 m² Let `a` be the length of side of the square. ⇒ a² = 484 ⇒ a = ⇒ a = 22 m Total length of the wire = Perimeter of the square = 4 x 22m = 88 m Perimeter of the square = Perimeter of equilateral triangle. ⇒ 3 x side = 88 m ⇒ side = m ⇒ side = 29.3 m Area of equilateral triangle = x side² = x (29.3)² m² = x 858.49 m² = 372.57 m² Hence, the area of the equilateral triangle is 372.57 sq. m. (ii) Given: Length of the rectangle = 16 m Let `b` be the breadth of the rectangle. Perimeter of the rectangle = Perimeter of the square ⇒ 2(l \+ b) = 88 m ⇒ 2(16 \+ b) = 88 m ⇒ 16 \+ b = m ⇒ 16 \+ b = 44 m ⇒ b = 44 \- 16 m ⇒ b = 28 m Area of the rectangle = l x b = 16 x 28 m² = 448 m² Hence, the area of the rectangle is 448 sq. m.

Mathematics

A wire when bent in the form of a square encloses an area of 484 m². Find the largest area enclosed by the same wire when bent to form :
(i) an equilateral triangle.
(ii) a rectangle of breadth 16 m.

Mensuration

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Mathematics

A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to form :(i) an equilateral triangle.(ii) a rectangle of breadth 16 m.

Mensuration

Related Questions

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A wire when bent in the form of a square encloses an area of 484 m². Find the largest area enclosed by the same wire when bent to form :
(i) an equilateral triangle.
(ii) a rectangle of breadth 16 m.

A footpath of uniform width runs all around the outside of a rectangular field 30 m long and 24 m wide. If the path occupies an area of 360 m², find its width.