Question

if AD=3x-2,AE=5x-4,BD=x+1 and EC=3x-1.Find value of x​

Answer 1

Answer:

x=1/$\sqrt{2$

Step-by-step explanation:

Hope ABC is a Triangle and DE is parallel to BC.

Considering the similar triangles ABC and ADE,

AD/AB=AE/AC

Given, AD=3x+2, DB=x+1, AE=5x+4, EC=3x-1

AB=AD+DB=4x+3, AC=AE+EC=8x+5

Thus, using the equation,

(3x+2)/(4x+3)=(5x+4)/(8x+5)

(3x+2)(8x+5)=(5x+4)(4x+3)

24$x^{2}$+31x+10=20$x^{2}$+31x+12

4$x^{2}$=2, x=1/$\sqrt{2$