The area of a rectangle is $640 m^{2}$ . If the perimeter of the rectangle is $104 m$ , find its dimensions.

l e n g t h = 32 m

and

B r e a d t h = 20 m

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l e n g t h = 12 m

and

B r e a d t h = 40 m

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l e n g t h = 40 m

and

B r e a d t h = 16 m

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l e n g t h = 30 m

and

B r e a d t h = 22 m

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Solution

The correct option is A $l e n g t h = 32 m$ and $B r e a d t h = 20 m$
Given,
Area of rectangle= $640 m^{2}$ and
Perimeter of rectangle= $104 m$
Let, length of the rectangle= $x c m$ and
Width of the rectangle= $y c m$
Therefore,
$x y = 640$
$=> y = \frac{640}{x}$
Therefore,
Width= $\frac{640}{x}$
Now,
$2 (x + y) = 104$
$=> x + y = 52$
$=> x + \frac{640}{x} = 52$
$=> x^{2} - 52 x + 640 = 0$
$=> x - 32 x - 20 x + 640 = 0$
$=> x - (x - 32) - 20 (x - 32) = 0$
$=> (x - 32) (x - 20) = 0$
Therefore,
$x = 32$ or, $x = 20$
Therefore,
$y = 20 m$ or, $y = 32 m$

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