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
B
3263 cm2
C
2563 cm2
D
2973 cm2

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 cmor, 3$$\times$$ side $$=$$ 96 cmor, 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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