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Question Number 214479 by Frangg last updated on 09/Dec/24

Answered by mehdee7396 last updated on 10/Dec/24

((5x−6)/(3x))=((26)/(18))=((13)/9) 45x−54=39x 6x=54⇒x=9

$$\frac{\mathrm{5}{x}−\mathrm{6}}{\mathrm{3}{x}}=\frac{\mathrm{26}}{\mathrm{18}}=\frac{\mathrm{13}}{\mathrm{9}} \\ $$$$\mathrm{45}{x}−\mathrm{54}=\mathrm{39}{x} \\ $$$$\mathrm{6}{x}=\mathrm{54}\Rightarrow{x}=\mathrm{9} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Answered by MATHEMATICSAM last updated on 10/Dec/24

If CD ∣∣ AB then ((AB)/(CD)) = ((BE)/(DE)) ⇒ ((5x − 6)/(3x)) = ((8 + 18)/(18)) ⇒ ((5x − 6)/(3x)) = ((26)/(18)) = ((13)/9) ⇒ 45x − 54 = 39x ⇒ 6x = 54 ⇒ x = 9

$$\mathrm{If}\:\mathrm{CD}\:\mid\mid\:\mathrm{AB}\:\mathrm{then} \\ $$$$\frac{\mathrm{AB}}{\mathrm{CD}}\:=\:\frac{\mathrm{BE}}{\mathrm{DE}} \\ $$$$\Rightarrow\:\frac{\mathrm{5}{x}\:−\:\mathrm{6}}{\mathrm{3}{x}}\:=\:\frac{\mathrm{8}\:+\:\mathrm{18}}{\mathrm{18}} \\ $$$$\Rightarrow\:\frac{\mathrm{5}{x}\:−\:\mathrm{6}}{\mathrm{3}{x}}\:=\:\frac{\mathrm{26}}{\mathrm{18}}\:=\:\frac{\mathrm{13}}{\mathrm{9}} \\ $$$$\Rightarrow\:\mathrm{45}{x}\:−\:\mathrm{54}\:=\:\mathrm{39}{x} \\ $$$$\Rightarrow\:\mathrm{6}{x}\:=\:\mathrm{54}\:\Rightarrow\:{x}\:=\:\mathrm{9}\: \\ $$

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