Adv
deepaksoni
  • 0
Guru

In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC.If AD = 8x – 7 cm, DB = 5x – 3 cm, AE = 4x – 3 cm, and EC = (3x – 1) cm, Find the value of x.

  • 0

Question taken from RD sharma
Class 10th
Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions.

In this question we have been given ΔABC,

D and E are points on the sides AB and AC respectively such that DE || BC.

Also it is given that AD = 8x – 7 cm, DB = 5x – 3 cm, AE = 4x – 3 cm, and EC = (3x – 1) cm, now we have to Find the value of x

 

Understanding and learning CBSE maths
RD sharma, DHANPAT RAI publication

Share

1 Answer

  1. Given:

    Length of side AD = 8x – 7, DB = 5x – 3, AER = 4x – 3 and EC = 3x -1

    To find : Value of x

    By using Thales Theorem, we get

    AD/BD = AE/CE                                       – equation 1

    Now, putting values in equation 1,

    (8x – 7)/(5x – 3) = (4x–3)/ (3x–1)

    (8x – 7)(3x – 1) = (5x – 3)(4x – 3)

    24x2 – 29x + 7 = 20x2– 27x + 9

    4x2 – 2x – 2 = 0

    2(2x2 – x – 1) = 0

    2x2 – x – 1 = 0

    2x2 – 2x + x – 1 = 0

    2x(x – 1) + 1(x – 1) = 0

    (x – 1)(2x + 1) = 0

    ⇒ x = 1 or x = -1/2

    Since, we know that the side of triangle is always positive.

    Therefore, we take the positive value.

    ∴ x = 1.

    Therefore, the value of x is 1.

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions