Question

what values of x will make DE parallel to AB in gives figure if AD=8x+9,CD=x+3,BE=3x+4,CE=x​

Answer 1

Answer:

Acc. to the parallelogram theorem,

CDbyDA=CEbyEB

Step-by-step explanation:

x+3 by 8x+9 = x by 3x+4

then,

Do, the cross-multiplication

You will get the answer.

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.