Question

Give possible values for length and breadth of the rectangle whose area is -x square+7x+30

Answer 1

I read that as
area = -x^2 + 7x + 30
this has to be positive, so
-x^2 + 7x + 30 > 0
x^2 - 7x - 30 < 0
(x - 10)(x+3) < 0

so you know that -3 < x < 10
that is, x must be between -3 and 10

Possible values :
let x = 1, then area = -1 + 7 + 30 = 36
the rectangle is 1 by 36/1 or 1 by 36

let x = 2, then area = -4 + 14 + 30 = 40
the rectangle is 2 by 40/2 or 2 by 20

etc, there will be an infinite number of cases