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

`a/(a+1)=b/(b+x)`

By cross multiplication on both sides, we get

`axx(b+x)=bxx(a+1)`

`ab+ax=ab+b`

`ax=ab+b-ab`

`ax=cancel(ab)+b-cancel(ab)`

`ax=b`

`x=b/a`

Hence the value of  x is  `b/a`