Question

ABCD is a trapezium in which $AB \parallel DC$. P and Q are points on sides AD and BC such that $PQ \parallel AB$. If PD = 18, BQ = 35 and QC = 15, find AD.

Answer 1

Answer:

The value of AD is 60  

Step-by-step explanation:

Given :  

In trapezium ABCD,  AB || CD . P & Q are points on sides AD and BC & PQ || AB .

PD = 18 , BQ = 35 , QC = 15  

Join AC  

In ∆ACD , OP || CD

AP/PD = AO/OC ………….(1)

[By using basic proportionality theorem]

In ∆ABC , OQ || AB

BQ/QC = AO/OC ………….(2)

[By using basic proportionality theorem]

From eq 1 and 2,

AP/PD = BQ/QC

AP/18 = 35/15

AP/18 = 7/3

3 AP = 18 × 7

AP = (18 × 7)/3

AP = 6 × 7

AP = 42  

AD = AP + PD

AD = 42 + 18

AD = 60  

Hence, the value of AD is 60  

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

$\huge\bold\pink{Solution}$

•REFER TO THE ATTACHMENT......

$\huge\underline\mathfrak{Final\:Answer}$

The length of AD is 60 cms.