Question

Find the value of ' x ' for which DE || AB in the above right sided Figure.​

Answer 1

$\huge \mathscr \blue{Answer}$

$\bf{If \:DE \: || \:AB, \: then \: \triangle CDE \: ∼ \: \triangle ABC }$

$\bf{By \: property \: of \: similar \: triangles:}$

$\bf{\frac{CD}{AC} = \frac{CE}{BC}}$

$\bf{⟹ \: \frac{x \: + \: 3}{4x \: + \: 22} = \: \frac{x}{4x \: + 4} }$

$\bf{Cross-multiplying:}$

$\bf{(x+3)(4x+4)=x(4x+22)}$

$\bf{⟹ \: {4x}^{2} \: + \: 16x \: + \: 12 \: = \: {4x}^{2} \: + \: 2x }$

$\bf{12=6x⟹ \: { \boxed{x \: = \: 2}}}$

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