Give possible expressions for the length(l) and breadth(b) of the rectangle whose area is given by $4 a^{2} + 4 a - 3$ .

l = 2 a + 3

b = 2 a - 1

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b = 2 a + 2

l = 2 a - 2

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b = 2 a + 3

l = 2 a - 1

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l = 2 a + 2

b = 2 a - 2

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Solution

The correct options are
A $l = 2 a + 3$ , $b = 2 a - 1$
C $b = 2 a + 3$ , $l = 2 a - 1$
Area of the rectangle is length $\times$ breath.
Given area $= 4 a^{2} + 4 a - 3$
The above expression can be written as
$= 4 a^{2} + 4 a - 3$
$= 4 a^{2} + 6 a - 2 a - 3$
$= 2 a (2 a + 3) - 1 (2 a + 3)$
$= (2 a + 3) (2 a - 1)$
Thus, one possible solution can be length $= (2 a + 3)$ and breath $= (2 a - 1)$
Another possible solution can be breadth $= (2 a + 3)$ and length $= (2 a - 1)$

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