AB, CD and EF are three parallel lines, in that order

Geometry

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1 : d2 = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

  1. slightly less than 10 units
  2. 10 units
  3. slightly greater than 10 units
  4. slightly less than 20 units
  5. slightly greater than 20 units

Answer

 

Area of the quadrilateral PQRS = 30

½2xy + ½xy = 30

xy = 20

So, for x yo be minimum, it should be 1.

∴ y = 20

So, QR = √(x2 + y2)

QR = √(202 + 12) = √401

which is slightly greater than 20.

The correct option is E.