V(x,y) is a point on the line segment from P(0,20) to Q(30,0) and a rectangle is constructed so that OV is one of its diagonals, where O has coordinates (0,0). If x is an integer, which of the following could not be the area of the rectangle?
(A) 54 (B) 108 (C) 126 (D) 144 (E) 150
Damn this is brutal..took me way more than 2 mins to solve, but here it is:
Equation of line PQ is:
y= - 2/3x + 20
=> V can be represented as (x, -2/3x+20)
If this is the diagonal, then the area is x*y = 20x -2/3x^2
Our requirement is to find x such that x is a +ve I.
From a,b,c,d,e we get 5 equations:
a. 20x - 2/3x^2 = 54
or 10x -x^2/3 = 27
or 30x - x^2 = 81
or x^2 - 30x + 81 = 0
x^2 -27x -3x +81 = 0
x= 27 or x=-3
b. 20x - 2/3x^2 = 108
or 10x-x^2/3 = 54
or 30x - x^2 = 162
or x^2 - 30x + 162 = 0
There are no whole roots for the above equation, therefore B is the answer. Look no further.