In Delta XYZ,X-S-Y,X-T-Z and overline{ST} 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

Vedclass · Accepted Answer

$11$

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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.In $\Delta XYZ$,since $\overline{ST} \parallel \overline{YZ}$,we have:$\frac{XS}{SY} = \frac{XT}{TZ}$Substitute the given values:$\frac{4}{x-4} = \frac{8}{3x-19}$Cross-multiply to solve for $x$:$4(3x - 19) = 8(x - 4)$$12x - 76 = 8x - 32$$12x - 8x = 76 - 32$$4x = 44$$x = 11$

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

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