Question

give possible values for length and breadth of the rectangle whose area is 4 a square + 2A - 6​

Answer 1

$area = 4 {a}^{2} + 2a - 6$

$area = 4 {a}^{2} - 4a + 6a - 6$

$area = 4a(a - 1) + 6(a - 1)$

$area = (a - 1)(4a + 6)$

so length and breadth takes the values (a-1) and (4a+6)

length and breadth should always be positive

so a-1>0, 4a+6>0

a>1 and a>-3/2

therefore, a takes all the values greater than 1

hence length takes all positive values and breadth takes all values greater than 10