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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:
- An equilateral triangle.
- A rectangle of length 16 m.
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Solution
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.
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