BC⎯⎯⎯⎯⎯ is parallel to DE⎯⎯⎯⎯⎯. What is AC? Enter your answer in the box. 34 units A triangle with vertices labeled as A, D, and

Question

4 years ago

5

BC⎯⎯⎯⎯⎯ is parallel to DE⎯⎯⎯⎯⎯. What is AC? Enter your answer in the box. 34 units A triangle with vertices labeled as A, D, and

E. Side D E is the base and the top vertex is A. Sides A D and A E contain midpoints B and C, respectively. A line segment is drawn from point B to C. Side A B is labeled as 8. Side B D is labeled as 10. Side C E is labeled as 15.

Mathematics

2 answers:

suter [353] · Answer 1 · 2022-02-09T02:31:31+03:00

suter [353]4 years ago

4 0

Answer:

AC: 12

Step-by-step explanation:

egoroff_w [7] · Answer 2 · 2022-02-09T00:12:08+03:00

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE, then angles D and B are congruent and angles C and E are congruent as well. This means that triangles ABC and ADE are similar by the AAA (or AA) similarity theorem.

We know that similar triangles are in proportion. This means that $\frac{AC}{AE} = \frac{AB}{AD}$

Now, we can plug the values given into that equation:

$\frac{x}{x+15} = \frac{8}{18}$

Now, cross multiply:

18x = 8(x + 15)

Now, we can simplify this equation and solve for x, or AC.

18x = 8x + 120

Subtract 8x from both sides:

10x = 120

Divide both sides by 10:

x = 12

Hope this helps!