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Question

A wire when bent in the form of a square encloses an area $$ = $$ 576 cm$$ ^{2} $$. Find the largest area enclosed by the same wire when bent to form an equilateral triangle.


A
3663 cm2
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B
3263 cm2
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C
2563 cm2
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D
2973 cm2
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Solution

The correct option is C $$ 256\sqrt{3} $$ cm$$ ^{2} $$
Given,A wire when bent in the form of a square encloses an area of 576 sq. m .
Area of Square$$= { (side) }^{ 2 } $$
or,         576     $$= { (side) }^{ 2 } $$    
or,        side      $$= \sqrt { 576 } = 24 cm$$  
Perimeter of square$$=$$ 4 $$\times$$ side
                                $$=$$ 4 $$\times$$ 24
                                $$=$$  96 cm.          
When same wire is formed into equilateral triangle,then perimeter of square is equals to perimeter of triangle.
$$\therefore$$ Perimeter of equilateral triangle$$=$$ 96 cm
or, 3$$\times$$ side $$=$$ 96 cm
or, side     $$=$$  $$\frac { 96 }{ 3 } =$$ 32 cm.
Area of equilateral triangle thus formed $$=\frac { \sqrt { 3 } \times { (side) }^{ 2 } }{ 4 } $$
                                                               $$=\frac { \sqrt { 3 } \times {  32 }^{ 2 } }{ 4 } $$
                                                               $$=\quad 256\sqrt { 3 } \quad { cm }^{ 2 } $$

Mathematics

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