Question

BC is parallel to DE.what is the length of CE?

Answer 1

Answer:

Option B $2\frac{2}{3}\ units$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and ADE are similar by AA Similarity Theorem

so

$\frac{AB}{AD}=\frac{AC}{AE}$

substitute the given values

$\frac{3}{3+2}=\frac{4}{AE}$

Solve for AE

$\frac{3}{5}=\frac{4}{AE}$

$AE=5(4)/3$

$AE=\frac{20}{3}\ units$

Find the length of CE

$AE=AC+CE\\CE=AE-AC$

substitute the values

$CE=\frac{20}{3}-4$

$CE=\frac{8}{3}\ units$

Convert to mixed number

$\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units$