ABCD is a trapezium in which AB parallel DC a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given,a trapezium $ABCD$ in which $AB \parallel DC$. $P$ and $Q$ are points on $AD$ and $BC$ respectively such that $PQ \parallel DC$. Thus,$AB \p

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(A) Given,a trapezium $ABCD$ in which $AB \parallel DC$. $P$ and $Q$ are points on $AD$ and $BC$ respectively such that $PQ \parallel DC$. Thus,$AB \parallel PQ \parallel DC$.Join $BD$. Let $BD$ intersect $PQ$ at point $O$.In $	riangle ABD$,$PO \parallel AB$ (since $PQ \parallel AB$).By the Basic Proportionality Theorem $(BPT)$,we have:$\frac{AP}{PD} = \frac{BO}{OD}$  .......$(i)$In $	riangle BDC$,$OQ \parallel DC$ (since $PQ \parallel DC$).By the Basic Proportionality Theorem $(BPT)$,we have:$\frac{BQ}{QC} = \frac{BO}{OD}$  .......$(ii)$From equations $(i)$ and $(ii)$,we get:$\frac{AP}{PD} = \frac{BQ}{QC}$Substitute the given values $PD = 18 \, cm$,$BQ = 35 \, cm$,and $QC = 15 \, cm$:$\frac{AP}{18} = \frac{35}{15}$$AP = \frac{35 	imes 18}{15}$$AP = \frac{7 	imes 18}{3} = 7 	imes 6 = 42 \, cm$Therefore,$AD = AP + PD = 42 \, cm + 18 \, cm = 60 \, cm$.

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

Similar Questions

It is given that $\triangle ABC \sim \triangle DFE$,$\angle A = 30^{\circ}$,$\angle C = 50^{\circ}$,$AB = 5 \, cm$,$AC = 8 \, cm$ and $DF = 7.5 \, cm$. Then,the following is true:

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $\frac{AB}{CD} = \frac{2}{1}$ and $AC = 15$,find $MA$ and $MC$.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides,then the two sides are divided in the same ratio.

The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : AB = 2 : 3$ and $AC = 15$,then $NC = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module