MATH SOLVE

5 months ago

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

Accepted Solution

A:

Answer:Option B [tex]2\frac{2}{3}\ units[/tex]Step-by-step explanation:we know thatIf two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruentIn this problem Triangles ABC and ADE are similar by AA Similarity Theoremso[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]substitute the given values[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]Solve for AE[tex]\frac{3}{5}=\frac{4}{AE}[/tex][tex]AE=5(4)/3[/tex][tex]AE=\frac{20}{3}\ units[/tex]Find the length of CE[tex]AE=AC+CE\\CE=AE-AC[/tex]substitute the values[tex]CE=\frac{20}{3}-4[/tex][tex]CE=\frac{8}{3}\ units[/tex]Convert to mixed number[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]