Question

In the Triangle ABC,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​

Answer 1

Answer:

Pls mark as Brainlist

Step-by-step explanation:

Given: AD = 8x – 7, DB = 5x – 3, AE = 4x – 3 and EC = 3x -1 Required to find x. By using Thales Theorem, [As DE ∥ BC] AD/BD = AE/CE (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 12 We know that the side of triangle can never be negative. Therefore, we take the positive value. ∴ x = 1.Read more on Sarthaks.com - https://www.sarthaks.com/634165/in-a-abc-and-are-points-on-the-sides-ab-and-ac-respectively-such-that-de-bc-if-ad-8x-7-cm-db-5x-cm