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Length of a rectangle is 8 cm longer than its width. A square of side x centimeters is cut out of it. If $‘ x ’$ centimeters is half the width of the rectangle, then the remaining area in square centimeters is

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3 x^{2} + 8 x

2 x^{2} + 16 x

3 x^{2} + 16 x

2 x^{2} + 8 x

answer is A.

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Detailed Solution

Given, $x = \frac{1}{2} b \Rightarrow b = 2 x$

Length of rectangle $= 8 + b$

$l = 8 + 2 x$

Area of rectangle $= l \times b$

$= (8 + 2 x) 2 x$

$= 4 x^{2} + 16 x$

Area of square $= x^{2}$

Area of remaining part $=$ Area of rectangle $-$ Area of square

$= 3 x^{2} + 16 x$

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