Question

In the figure if DE parallel to BC and AD = 4x - 3 , AE = 8x-7 , BD = 3x - 1 and EC = 5x - 3 . Find the value of x

Answer 1

Answer:

The value of x is 1

Step-by-step explanation:

In the figure if DE parallel to BC and AD = 4x - 3 , AE = 8x-7 , BD = 3x - 1 and EC = 5x - 3 . Find the value of x

Basic proportionality theorem(Thales theorem):

If a line is drawn parallel to one side of a triangle then it cuts other two sides proportionally.

In $\triangle\:ABC, DE\parallel\:BC$

By Thales theorem,

$\frac{AD}{BD}=\frac{AE}{EC}$

$\implies\:\frac{4x-3}{3x-1}=\frac{8x-7}{5x-3}$

$\implies\:(4x-3)(5x-3)=(3x-1)(8x-7)$

$\implies\:20x^2-27x+9=24x^2-29x+7$

$\implies\4x^2-2x-2=0$

$\implies\2x^2-2x+x--1=0$

$\implies\2x(x-1)+1(x--1)=0$

$\implies\(2x+1)(x--1)=0$

$\implies\x=\frac{-1}{2},1$

But x cannot be negative

The value of x is 1

Answer 2

Given, DE//AB

$\frac{AD}{DC} = \frac{BE}{EC} \\ \\ \frac{8x + 9}{x + 3} = \frac{3x + 4}{x} \\ \\ {8x}^{2} +9x= {3x}^{2} +13x+12 \\ \\ {5x}^{2} −4x−12=0 \\ \\ {5x}^{2} −10x+6x−12=0 \\ \\ 5x(x−2)+6(x−2)=0 \\ \\ (5x+6)(x−2)=0 \\ \\ x = \frac{ - 6}{5} \: and \: 2$

Therefore x is 2.