Question

In the triangle DEF where E is the midpoint, DE = 6x + 1 and EF = 7x - 4. Find DE, EF, and DF.

A) DE = 8, EF = 9, DF = 17
B) DE = 9, EF = 10, DF = 19
C) DE = 10, EF = 11, DF = 21
D) DE = 11, EF = 12, DF = 23

Answer 1

After setting the expressions DE = 6x + 1 and EF = 7x - 4 equal to each other because E is the midpoint, we find x to be 5. Thus, DE = EF = 31, and DF = 62. None of the answer choices provided match these results.

Step-by-step explanation:

To find the lengths of sides DE, EF, and DF in triangle DEF, we need to use the information that E is the midpoint of DF. This gives us a clue that DE and EF are equal since E is the midpoint. Given that DE = 6x + 1 and EF = 7x - 4, we can set these two expressions equal to each other because DE = EF.

6x + 1 = 7x - 4
Solving for x, we subtract 6x from both sides:

x = 5

Now, plug x = 5 back into the expressions for DE and EF:

DE = 6(5) + 1 = 30 + 1 = 31
EF = 7(5) - 4 = 35 - 4 = 31

Since DE = EF, then the length of DF, which includes DE and EF, is:

DF = DE + EF = 31 + 31 = 62

Thus, DE = 31, EF = 31, and DF = 62. None of the answer choices (A, B, C, D) match our findings, so there seems to be an error in the question or the options provided.