Question

In each of the figure, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segments are marked. Find the value of $x$ in each of the following :

Answer 1

Basic proportionality theorm :
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.

$\left(i\right)$ $\frac{1}{c}=\frac{d}{x}$

$\therefore$ $x=cd$

$\left(ii\right)$ $\frac{a}{1}=\frac{b}{x}$

$\therefore$ $x=\frac{b}{a}$

$\left(iii\right)$ $\frac{1}{g}=\frac{g}{x}$

$\therefore$ $x=g^2$

$\left(iv\right)$ $\frac{1}{x}=\frac{h}{1}$

$\therefore$ $x=\frac{1}{h}$