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 from:

1. An equilateral triangle.
2. A rectangle of length 16 m.

Answer 1

The area of the square is 484.

Let a be the length of each side of the square.

Now

a² = 484 

a = 22 m

Hence, the length of the wire is = 4 × 22 = 88 m.

(i) Now, this 88 m wire is bent in the form of an equilateral triangle.

Side of the triangle = `88/3`

= 29.3 m

Area of the triangle = `sqrt3/4` × (Side)²

= `sqrt3/4` × (29.3)²

= 372.58 m²

(ii) Let x be the breadth of the rectangle.

Now,

2(l + b) = 88

16 + x = 44

x = 28 m

Hence, area = 16 × 28 = 448 m².