Give possible expressions for the length and breath of the rectangle whose area is- 4a2+4a-3.

# Give possible expressions for the length and breath of the rectangle whose area is- $4{a}^{2}+4a-3$.

1. A
$\left(2a-3\right)\left(2a+3\right)$
2. B
$\left(2a-1\right)\left(2a-3\right)$
3. C
$\left(2a+3\right)\left(2a-1\right)$
4. D
None of these

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Concept- A rectangle is a type of parallelogram whose all angles are right angles, especially the one with adjacent sides of unequal length, and  has area equal to the product of its length and breadth.
Option 1)
$=2a\left(2a+2\right)-3\left(2a+2\right)$
$=4{a}^{2}+4a-6a-6$
$=4{a}^{2}-2a-6$
As, $4{a}^{2}-2a-6\ne 4{a}^{2}+4a-3$
Option 2) (2a-1)(2a-3)
$=2a\left(2a-3\right)-1\left(2a-3\right)$
$=4{a}^{2}-6a-2a+3$
$=4{a}^{2}-8a+3$
As, $4{a}^{2}-8a+3\ne 4{a}^{2}+4a-3$
Option 3) $\left(2a+3\right)\left(2a-1\right)$
$=2a\left(2a-1\right)+3\left(2a-1\right)$
$=4{a}^{2}-2a+6a-3$
$=4{a}^{2}+4a-3$
As, $4{a}^{2}+4a-3=4{a}^{2}+4a-3$
Hence, the correct answer is option 3.

## Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)