AB, CD and EF are three parallel lines, in that order. Let d_{1} and d_{2} be the distances from CD to AB and EF respectively. d_{1} and d_{2} are integers, where d_{1} : d_{2} = 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?

- slightly less than 10 units
- 10 units
- slightly greater than 10 units
- slightly less than 20 units
- 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 = √(x^{2} + y^{2})

QR = √(20^{2} + 1^{2}) = √401

which is slightly greater than 20.

**The correct option is E.**

- The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is
- There are 24 equally spaced points lying on the circumference of a circle
- In a circle, two parallel chords on the same side of a diameter
- Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides
- Let ABCD be a rectangle inscribed in a circle of radius 13 cm