Question

In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :

Answer 1

${\displaystyle \frac{1}{1+h}=\frac{x}{x+1}}$

By cross multiplication on both sides, we get

${\displaystyle 1\times (x+1)=x\times (1+h)}$

${\displaystyle x+1=x+hx}$

${\displaystyle x+1-x=hx}$

${\displaystyle \cancel{x}+1-\cancel{x}=hx}$

${\displaystyle 1=xh}$

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

Hence the value of x is ${\displaystyle \frac{1}{h}}$.