Home
Class 10
MATHS
In DeltaABC, seg BD bisects /ABC. If AB=...

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

Text Solution

Verified by Experts

In `DeltaABC`,
seg `BD` bisects `/_ABC`
`:.` by the 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`
Promotional Banner

Topper's Solved these Questions

  • SIMILARITY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 2.5 (4 mark each)|3 Videos

  • SIMILARITY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLE TYPE|50 Videos

  • SIMILARITY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 2.3 (2 mark each)|10 Videos

  • QUADRATIC EQUATIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise ASSIGNEMENT 2.4|8 Videos

  • STATISTICS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLES FOR PRACTICE (MCQs)|35 Videos

Similar Questions

Explore conceptually related problems

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

If AB||DC and AD||BC Find the value of x and y

In Delta ABC,AD=BC. Find x

In Delta ABC,AD=BC. Find x

In Delta ABC , DE || BC. If AD = 2x - 1, AE = 2x + 5, BD = x - 3 and CE = x - 1, then the value of x is:

In figure , DE||BC .If AD=x+1 , DB = x-2 , AE =x+2andEC =x+3 , find the value of x .

In Figure,DE|BC, if AD=x,DB=x-2,AE=x+2 and EC=x-1, find the value of x

In the figure Delta ABC, DE||AB . If AD = 2x, DC = x + 3, BE = 2x - 1 CE = x then find the value of x .

In Fig. 7.11, Deabs()BC . If AD= x, DB= x- 2, AE = x + 2 and EC =x -1, find the value of x.