Question

ABCD is a trapezium in which AB || DC and P and Q are the points on AD and BC, respectively, such that PQ || DC. If PD = 18 cm, BQ = 35 cm and QC = 15 cm, then AD = ______.

Answer 1

ABCD is a trapezium in which AB || DC and P and Q are the points on AD and BC, respectively, such that PQ || DC. If PD = 18 cm, BQ = 35 cm and QC = 15 cm, then AD = 60 cm.

Explanation:

Let the three parallels be AB, PQ and DC. They cut the transversals AD and BC proportionally, so `(AP)/(PD) = (BQ)/(QC)`.

Given BQ : QC = 35 : 15 = 7 : 3 and PD = 18.

So `AP = 7/3 xx PD`

= `7/3 xx 18`

= 42 cm

Therefore AD = AP + PD

= 42 + 18

= 60 cm