Question

in the figure above, $overline{af}$, $overline{be}$, and $overline{cd}$ are parallel. points $b$ and $e$ lie on $overline{ac}$ and $overline{fd}$, respectively. if $ab = 9, bc = 18.5$, and $fe = 8.5$, what is the length of $overline{ed}$, to the nearest tenth?
a 16.8
b 17.5
c 18.4
d 19.6

Explanation:

Step1: Apply parallel - line proportion rule

Since $\overline{AF}\parallel\overline{BE}\parallel\overline{CD}$, we have the proportion $\frac{AB}{BC}=\frac{FE}{ED}$.

Step2: Substitute given values

Substitute $AB = 9$, $BC = 18.5$, and $FE = 8.5$ into the proportion: $\frac{9}{18.5}=\frac{8.5}{ED}$.

Step3: Cross - multiply

Cross - multiplying gives $9\times ED=8.5\times18.5$.

Step4: Solve for $ED$

$ED=\frac{8.5\times18.5}{9}=\frac{157.25}{9}\approx17.5$.

Answer:

B. 17.5