Question

figure PQ parallel to BC if PQ by BC is equal to 2 by 5 then AP by PB​

Answer 1

Given data:

In the figure $\mathsf{PQ||BC}$ and $\mathsf{\dfrac{PQ}{BC}=\dfrac{2}{5}}$

To find:

$\mathsf{\dfrac{AP}{PB}}$

Step-by-step explanation:

From the given figure, we can say that $\mathsf{\Delta APQ}$ and $\mathsf{\Delta ABC}$ are like triangles.

Then $\mathsf{\dfrac{AP}{AB}=\dfrac{PQ}{BC}}$

$\mathsf{\Rightarrow \dfrac{AP}{AP+PB}=\dfrac{2}{5}}$

Since $\mathsf{\dfrac{PQ}{BC}=\dfrac{2}{5}}$ and $\mathsf{AB=AP+PB}$

$\mathsf{\Rightarrow \dfrac{AP+PB}{AP}=\dfrac{5}{2}}$

$\mathsf{\Rightarrow 1+\dfrac{PB}{AP}=\dfrac{5}{2}}$

$\mathsf{\Rightarrow \dfrac{PB}{AP}=\dfrac{5}{2}-1}$

$=\dfrac{5-2}{2} =\dfrac{3}{2}}$

Answer: Option b) $\mathsf{\dfrac{AP}{PB}=\dfrac{2}{3}}$

Answer 2

If AP:PB=1:2 then AP:AB will be 1:3.

So, in similar triangles, the ratio of the area of ΔABCΔAPQ=(31)2=91