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Question
ABCD is a trapezium in which AB || DC and P, Q are points on AD and BC respectively, such that PQ || DC if PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD
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Solution
Join AC intersecting PQ at S.
Let AP be x
∴ AD = x + 18
In the ∆ABC, QS || AB
By basic proportionality theorem.
`"AS"/"SC" = "BQ"/"QC"`
`"AS"/"SC" = 35/15` ...(1)
In the ∆ACD; PS || DC
By basic proportionality theorem.
`"AS"/"SC" = "AP"/"PD"`
`"AS"/"SC" = x/18` ...(2)
From (1) and (2) we get
`35/15 = x/18`
15x = 35 × 18 ⇒ x = `(35 xx 18)/15` = 42
AD = AP + PD
= 42 + 18 = 60
The value of AD = 60 cm
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