159k views
4 votes
PLEASE HELP!!! Find the length of the midsegment to the nearest tenth.

PLEASE HELP!!! Find the length of the midsegment to the nearest tenth.-example-1

1 Answer

3 votes

Answer:

Midsegment is 35.

Explanation:

TL; DR:

The smaller triangle (with a base of 6x + 5) has side lengths that are twice as small as the entire triangle (the one with a base of 3x+55). So, 2(6x+5) = 3x + 55. x = 5, so the midsegment is 35.

Look at the photo attached below.

Here is the statement/reason:

1. ED ║ AB (Midsegments are parallel to the base)

Note: Then, CA and CB are transversals

2. Then, m∠CED = m∠EAB (corresponding angles)

3. m∠CDE = m∠DBA (corresponding angles)

4. ΔCED is similar to ΔCAB (angle angle)

5. CA = CE + EA

6. CA = 39 + 39 = 78 (Substitution, algebra)

7. ED/AB = CE/CA (similar triangles)

Note: You can also use CD and CB

8. (6x+5) / (3x+55) = 39 / 78 (substitution)

9. (6x + 5) / (3x + 55) = 1 / 2 (algebra)

10. 12x + 10 = 3x + 55, x = 5 (algebra)

11. ED = 6x + 5 (given)

12. ED = 6*5 + 5 = 35 (substitution, algebra)

An explanation of the algebra:

(6x+5) is twice as small as (3x + 55). So, we can write this equation:

2(6x+5) = 3x + 55

12x + 10 = 3x + 55

Subtract 3x from both sides.

9x + 10 = 55

Subtract 10 from both sides.

9x = 45

x = 5.

Now, put that into ED.

6x + 5 = 6 * 5 + 5 = 35

I hope this helps! Feel free to ask any questions!

PLEASE HELP!!! Find the length of the midsegment to the nearest tenth.-example-1
User Kiefer
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories