In Delta ABC,A-M-B,A-N-C and overline{MN} par | vedclass

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(D) According to the Basic Proportionality Theorem (Thales Theorem),if a line is drawn parallel to one side of a triangle to intersect the other two s

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$5$

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(D) According to the Basic Proportionality Theorem (Thales Theorem),if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points,then the other two sides are divided in the same ratio.Since $\overline{MN} \parallel \overline{BC}$,we have:$\frac{AM}{MB} = \frac{AN}{NC}$Substitute the given values:$\frac{x+1}{x} = \frac{3x-3}{4x-10}$Cross-multiply to solve for $x$:$(x+1)(4x-10) = x(3x-3)$$4x^2 - 10x + 4x - 10 = 3x^2 - 3x$$4x^2 - 6x - 10 = 3x^2 - 3x$$x^2 - 3x - 10 = 0$Factor the quadratic equation:$(x-5)(x+2) = 0$This gives $x = 5$ or $x = -2$.Since length cannot be negative,$x$ must be $5$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x+1$,$MB = x$,$AN = 3x-3$ and $NC = 4x-10$,then $x = \dots$

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