Question

In the figure PQ\\BC,if PQ/BC=2/5, then AP/PB is
a)2/5
b)2/3
c)3/2
d)3/5​

Answer 1

given,

$PQ/BC=2/5\\AP/PB\\=?\\PQ=2\\BC=5\\AP=PQ=2\\BC=AB\\BC=5=AB\\BP=AB-AP\\=5-2\\=3\\BP=3\\AP/PB=2/3$

Hence, the correct option is (b) 2/3 .

Answer 2

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 $\mathsf{AB=AP+PB}$

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

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

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

$\mathsf{\Rightarrow \dfrac{PB}{AP}=\dfrac{5-2}{2}=\dfrac{3}{2}}$

$\mathsf{\Rightarrow \dfrac{AP}{PB}=\dfrac{2}{3}}$

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

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