Question

in the diagram below, \\(\overline{ef}\\) is parallel to \\(\overline{bc}\\). solve for \\(x\\). round your answer to the nearest tenth if necessary.\
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(diagram with triangle dbc, point e on db, point f on dc. de = 19.6, eb = 16.4, df = 24.5, fc = x)\
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answer attempt 1 out of 2\
\\(x = \square\\)\
submit answer

Explanation:

Step1: Identify Similar Triangles

Since $\overline{EF} \parallel \overline{BC}$, by the Basic Proportionality Theorem (Thales' theorem), $\triangle DEF \sim \triangle DBC$. Thus, the ratios of corresponding sides are equal: $\frac{DE}{DB}=\frac{DF}{DC}$.

Step2: Calculate Length of DB

First, find $DB = DE + EB = 19.6 + 16.4 = 36$.

Step3: Set Up Proportion

Substitute the known values into the proportion: $\frac{19.6}{36}=\frac{24.5}{24.5 + x}$.

Step4: Cross - Multiply and Solve for x

Cross - multiply: $19.6(24.5 + x)=36\times24.5$.
Expand the left side: $19.6\times24.5+19.6x = 36\times24.5$.
Calculate $19.6\times24.5 = 480.2$ and $36\times24.5 = 882$.
So, $480.2+19.6x = 882$.
Subtract 480.2 from both sides: $19.6x=882 - 480.2=401.8$.
Divide both sides by 19.6: $x=\frac{401.8}{19.6}\approx20.6$.

Answer:

20.6