Xavier Aptitude Test 2016 Paper

Question : 69 of 103

Marks: +1, -0

ABCD is a quadrilateral such that AD = 9 cm, BC = 13 cm and ∠DAB = ∠BCD = 90°. P and Q are two points on AB and CD respectively, such that DQ:BP = 1:2 and DQ is an integer. How many values can DQ take, for which the maximum possible area of the quadrilateral PBQD is 150 sq. cm?

Validate

Solution:

(d)

Let DQ = x, CQ = y, AP = z.
Then BP = 2x
Area of PBQD = Area of the quadrilateral ABCD – (Area
of triangle ΔAPD + Area of Δ BCQ) ....(1)
Area of ABCD = Area of ΔABD + Area of ΔBCD ....(2)

∴

Area of

\ {PBQD}= [\ {1}{2} \×(2 \ {x}+\ {z}) × 9+ {1}/{2} \× 13 \×(\ {x}+\ {y})\ ]

- [\ {1}/{2}× 9 \× \ {z}+ {1}/{2} × 13 × \ {y}\ ]

=\ {31 \ {x}}/{2}

\ {31 {x}}/{2}≤ 150

{x} ≤ 9.68

\∴\ {x}

can take 9 integer values

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