AB|| DC where P, Q are points on AD and BC, respectively, such that PQ || DC, making ABCD a trapezium. Find AD if PD = 18 cm, BQ = 35 cm, and QC = 15 cm.

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AB|| DC where P, Q are points on AD and BC, respectively, such that PQ || DC, making ABCD a trapezium. Find AD if PD = 18 cm, BQ = 35 cm, and QC = 15 cm.

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52cm

58cm

60cm

47cm

answer is C.

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Detailed Solution

In triangle ABD

$DP / AP = OD / OB$

In triangle B D C

$B Q / Q C = O B / O D$

This implies

$DP / AP = QC / BQ$

$18 / A P = 15 / 35$

$A P = (18 \times 35) / 15$

$A P = 42$

Therefore, $AD = AP + DP = 42 + 18 = 60 cm$

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