Give possible expression for the length and breadth of the rectangle whose area is : $4 a^{2} + 4 a - 3$

(2 a - 3) (2 a + 2)

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(2 a - 1) (2 a - 3)

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(2 a + 3) (2 a - 1)

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None of the above

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Solution

The correct option is C $(2 a + 3) (2 a - 1)$
Given area of rectangle $=$ $4 a^{2} + 4 a - 3$
Let length and breadth of rectangle $l$ and $b$
Then area of rectangle $= l b =$ $4 a^{2} + 4 a - 3$
$= (2 a)^{2} + 6 a - 2 a - 3$
$= 2 a (2 a + 3) - 1 (2 a + 3)$
$= (2 a + 3) (2 a - 1)$
So, length is $(2 a + 3)$
And breadth is $(2 a - 1)$ .

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