In Delta ABC,A-D-B,A-E-C and overline{DE} par | vedclass

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(A) 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

$6$

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(A) 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,the other two sides are divided in the same ratio.Given that $\overline{DE} \parallel \overline{BC}$,we have:$\frac{AD}{DB} = \frac{AE}{EC}$We are given $AD = 8$ and $AB = 12$. Since $A-D-B$,we have $DB = AB - AD = 12 - 8 = 4$.Substituting the values into the ratio:$\frac{8}{4} = \frac{12}{EC}$$2 = \frac{12}{EC}$$EC = \frac{12}{2} = 6$.Therefore,the length of $EC$ is $6$.

In $\Delta ABC$,$A-D-B$,$A-E-C$ and $\overline{DE} \parallel \overline{BC}$. If $AD = 8$,$AB = 12$ and $AE = 12$,find $EC$.

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