Question

What value of x will make DE//AB,in the given figure?AD=8x+9,CD=x+3 BE=3x+4,CE=x.

Answer 1

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Answer 2

Answer:

The value of x is 2

Step-by-step explanation:

Step 1: Given Data DE IS Parallel to AB, AD=8X+9, CD=X+3.BE=3X+4, CE=X

Step 2: $\frac{C D}{D A}=\frac{C E}{E B}$ (Therefore CD/DA is equal to CE/EB)

Step 3: $\frac{x+3}{8 x+9}=\frac{x}{3 x+4}$(Cross Multiplication on both sides)

Step 4: To calculate the value of x

(x+3) x (3x+4)=(x) x (3x+9)

$\begin{array}{l}{3 x^{2}+4 x+9 x+12=8 x^{2}+9 x} \\ {3 x^{2}+13 x+12-8 x^{2}-9 x=0}\end{array}$

Step 5: $-5 x^{2}+4 x+12=0$

$5 x^{2}-4 x-12=0$  (Multiply – sign on both the sides)

$5 \mathrm{x}^{2}-10 \mathrm{x}+6 \mathrm{x}-12=0$

5x(x-2)+6(x-2)=0

(x-2)(5x+6)=0

Step 6: x-2=0  (Assign x-2 is equal to zero)

x=2