In `DeltaABC` set BD bisects `/_ABC`. If `AB-x, BC=x+5, AD=x-2, DC=x+2`, then find the value of x.

Explanation

In `DeltaABC`,
set BD bisects `/_ABC`
`:.` by theorem of angle bisector of a triangle,
`(AB)/(BC)=(AD)/(DC)`
`:.x/(x+5)=(x-2)/(x+2)`
`:.x(x+2)=(x-2)(x+5)`
`:.x^(2)+2x=x(x+5)-2(x+5)`
`:.x^(2)+2x=x^(2)+5x-2x-10`
`:.2x=3x-10`
`:.2x-3x=-10`
`:.-x=-10`
`:.x=10`
The value of x is 10.