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ABCD is a trapezium in which AB||DC and P and 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

Solution:

Given, ABCD is a trapezium in which AB||DC

P and Q are the points on AD and BC such that PQ||DC

We have to find the length of AD.

abcd-is-a-trapezium-in-which-ab-dc-and-p-and-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

Given, PD = 18 cm

BQ = 35 cm

QC = 15cm

Also, AB||PQ||DC

Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

In △ABD,

Given, AB||PQ

So, PO||AB

By BPT, DP/AP = OD/OB -------------- (1)

In △BDC,

Given, DC||PQ

So, OQ||DC

By BPT, OB/OD = BQ/QC

On rearranging,

OD/OB = QC/BQ --------------------------- (2)

Equating (1) and (2),

DP/AP = QC/BQ

So, 18/AP = 15/35

AP(15) = 35(18)

AP = 7(18)/3

AP = 42 cm

We know, AD = DP + AP

AD = 18 + 42

AD = 60 cm

Therefore, the length of AD is 60 cm.

✦ Try This: In trapezium ABCD, AB||DC and L is the mid-point of BC. Through L, a line PQ||AD has been drawn which meets AB in P and DC produced in Q. Prove that ar (ABCD) = ar (APQD)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 9

ABCD is a trapezium in which AB||DC and P and 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

Summary:

ABCD is a trapezium in which AB||DC and P and Q are 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

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