In Delta XYZ,X-P-Y,X-Q-Z and overline{PQ} par | vedclass

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(B) 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

$3.5$

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(B) 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.Given $\overline{PQ} \parallel \overline{YZ}$ in $\Delta XYZ$,we have:$\frac{XP}{PY} = \frac{XQ}{QZ} = \frac{3}{5}$.Let $XQ = 3k$ and $QZ = 5k$.We know that $XZ = XQ + QZ = 5.6$.Substituting the values,$3k + 5k = 5.6$.$8k = 5.6$.$k = \frac{5.6}{8} = 0.7$.Now,$QZ = 5k = 5 	imes 0.7 = 3.5$.

In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XP:PY = 3:5$ and $XZ = 5.6$,find $QZ$.

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