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

`x/(x+g)=g/(g+1)`

By cross multiplication on both sides, we get

`x xx(g+1)=gxx(x+g)`

`xg+x=gx+g^2`

`x= gx +g^2-gx`

`x= cancel(gx)+g^2-cancel(gx)`

`x= g^2`

Hence the value of  x is  `g^2`.