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?
Explanation:
Let DQ = x and PB = 2x.
From the diagram A(△BDP) = ½ × AD × PB = ½ × 9 × 2x.
Also A(△BDQ) = ½ × BC × DQ = ½ × 13 × x
A(ꐎBPDQ) = A(△BDQ) + A(△BDP) = ½ × 31 × x = 150
∴ x = 300 / 31
∴ x can have integer values from 1 to 9.
Hence , there are 9 values of DQ.
Hence, option (d).
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