TheCATExam
Sign in

XAT 2017 — QA & DI Question 16

Basics of QuadrilateralsMedium

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?

Answer & solution

  • A

    slightly less than 10 units

  • B

    10 units

  • C

    slightly greater than 10 units

  • D

    slightly less than 20 units

  • slightly more than 20 units

Solution

​​​​​​​

Let d1 = x and d2 = 2x.

Now, SR would be shortest when SR = d1 = x

Area of PQRS = 30 square units.

∴ Area of PQRS = ½ × QS × 2x + ½ × QS × x

= (3/2) × QS × x = 30 

⇒ QS × x = 20

Smallest value of x = 1 units.

⇒ QS = 20

∴ ∆QSR is right angled at S

⇒ QR2 = QS2 + SR2

⇒ QR2 = 400 + 1

⇒ QR = slightly more than 20.

Hence, option (e).

XAT 2017 QA & DI Q16: AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF res — Solution | TheCATExam