Question

In the following figure, line \[PY\parallel {\text{side }}BC\], AP=3, PB=6, AY=5, YC=x, and then find x.

Answer 1

Hint: Here we will find the value of x using the basic proportionality theorem i.e.., $\dfrac{{AY}}{{YC}} = \dfrac{{AP}}{{PB}}$

Complete step-by-step answer:

Since $PY\parallel BC$, Using basic proportionality theorem $\dfrac{{AY}}{{YC}} = \dfrac{{AP}}{{PB}}$
$
   \Rightarrow \dfrac{5}{x} = \dfrac{3}{6} \\
   \Rightarrow \dfrac{5}{x} = \dfrac{1}{2} \\
   \Rightarrow x = 10 \\
$
So this is your required answer.

Note: Basic proportionality theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.