Question

Please Help only option without explanation would also work​

Answer 1

Answer :

›»› AD = 60 cm

Given :

• 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, QC = 15 cm

To Find :

• AD = ?

Required Solution :

Here in this question we have to find AD. So, firstly we have to consider the AP as an variable, after that we will find AD on the basis of conditions given above.

Join AC intersecting PQ at s

Let ,

The AP be "x"

In the ∆ ABC, QS || AB

By basic proportionality theorem,

$\tt{:\implies \dfrac{AS}{SC} = \dfrac{BQ}{QC}}$

$\tt{:\implies \dfrac{AS}{SC} = \dfrac{35}{15}} \bf{\: \: \: \: ---- (1)}$

In the ∆ACB, PS || DC

By basic proportionality theorem,

$\tt{:\implies \dfrac{AS}{SC} = \dfrac{AP}{PD}}$

$\tt{:\implies \dfrac{AS}{SC} = \dfrac{x}{18}}\bf{\: \: \: \: ----(2)}$

From equation (1) and equation (2) we get

$\tt{: \implies \dfrac{35}{15} = \dfrac{x}{18} }$

$\tt{: \implies 15x = 35 \times 18}$

$\tt{: \implies x = \dfrac{35 \times 18}{15}}$

$\tt{: \implies x = \dfrac{360}{15}}$

$\bf{: \implies x = 42}$

Now ,

$\tt{: \implies AD = AP + PD}$

$\tt{: \implies AD = 42 + 18}$

$\bf{: \implies \underline{ \: \: \underline{ \red{ \: AD = 60 cm \: }} \: \: }}$

Hence Solved !