Question

HELP ME!!! Solve for X. Show all work to receive credit!

Answer 1

Answer:

$x=9.5\ units$

Step-by-step explanation:

The complete question is

Segment BC is parallel to segment DE. Find the value of x

we know that

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

In his problem

Triangle ABC is similar to Triangle ADE by AA Similarity Theorem

so

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

substitute the given values

$\frac{x+3+x-2}{x-2}=\frac{5+3}{3}$

solve for x

$\frac{2x+1}{x-2}=\frac{8}{3}$

$6x+3=8x-16\\8x-6x=3+16\\2x=19\\x=9.5$