Question

ABCD is a trapezium in which AB II CD and P, Q are points on AD and BC
respectively such that PQ II DC. If PD=18 cm, BQ=35 cm and QC=15 cm, find AD
(See figure)
35 cm
PIETRO
119 common
(A) 55cm
(B) 57 m
(C) 60cm
(D) 62cm​

Answer 1

Step-by-step explanation:

Given, A trapezium, ABCD in which AB‖DC, P and Q are Points on AD and BC respectively, Such that PQ || DC. Thus, AB||PQ||DC. In ∆ABD, PO || AB [∵ PQ || AB] By basic proportionality theorem, If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio. → AP = 42 ∴ AD = AP + DP AD = 42 + 18 = 60 So, AD = 60 cm