A wire when bent in the form of a square encloses an area of $484 m^{2}$ . Find the largest area enclosed by the same wire when bent to form a rectangle of breadth $16 m$ .

448 m

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428 m

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400 m

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456 m

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Solution

The correct option is A $448 m$
Given: A wire when bent in the form of a square encloses an area $= 484 c m^{2}$
We know Area of square $= {(side)}^{2}$
${(side)}^{2} = 484$
$side = 22 c m$
And
We know perimeter of square $= 4 \times side = 4 \times 22 = 88 c m$
And now same wire when bent to form a rectangle whose breadth is $16 c m$ .
So, Let length of formed rectangle $= x$
And we know perimeter of rectangle $= 2 (Length + Breadth)$ , so we get
$\Rightarrow 2 (x + 16) = 88$
$\Rightarrow x + 16 = 44$
$\Rightarrow x = 44 - 16$
$\Rightarrow x = 28$
So length of formed rectangle $= 28 c m$
Given Breadth of Rectangle $= 16 c m$
And Area of Rectangle $= 28 \times 16 = 448 c m^{2}$

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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 a rectangle of breadth 16 m.

A wire when bent in the form of a square encloses an area of $484 m^{2}$ . Find the largest area enclosed by the same wire when bent to form a rectangle of breadth $16 m$ .