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

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(A) Given that in $\Delta XYZ$,$\overline{PQ} \parallel \overline{YZ}$.According to the Basic Proportionality Theorem (Thales Theorem),if a line is dr

Vedclass · Accepted Answer

$6$

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(A) Given that in $\Delta XYZ$,$\overline{PQ} \parallel \overline{YZ}$.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.Therefore,$\frac{XP}{PY} = \frac{XQ}{QZ}$.We are given $XP = 8$ and $XY = 12$.Since $X-P-Y$,we have $PY = XY - XP = 12 - 8 = 4$.Now,substitute the values into the ratio: $\frac{8}{4} = \frac{12}{QZ}$.$2 = \frac{12}{QZ}$.$QZ = \frac{12}{2} = 6$.Thus,the value of $QZ$ is $6$.

In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XP = 8$,$XY = 12$ and $XQ = 12$,find $QZ$.

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