Question

E is the midpoint of DF, DE = 3x + 4 and EF = 5x - 2. Find DE, EF, and DF.

Answer 1

DE = 13, EF = 13, DF = 26

Step-by-step explanation:

To find the lengths of DE, EF, and DF, we can use the fact that E is the midpoint of DF. Since E is the midpoint, the lengths of DE and EF will be equal. Set them equal to each other:

3x + 4 = 5x - 2

Simplify and solve for x:

2x = 6

x = 3

Now substitute the value of x back into the expressions for DE and EF:

DE = 3x + 4 = 3(3) + 4 = 13

EF = 5x - 2 = 5(3) - 2 = 13

Since DE and EF are equal, we can find DF by adding their lengths:

DF = DE + EF = 13 + 13 = 26

Answer 2

Since E is the midpoint of DF, DE and EF are two halves of DF. First, let's write down what we know.

DE = 3x + 4

EF = 5x - 2

DE = EF

DE + EF = DF

Now, let's plug our values for DE and EF into our first expression.

3x + 4 = 5x -2

Add 2 to both sides and subtract 3x from both sides.

6 = 2x

Divide both sides by 2

3 = x

Let's plug 3 in for x into DE.

DE = 3x + 4 = 3(3) + 4 = 9 + 4 = 13

DE = EF = 13

We can plug 13 in for DE and EF to get DF

DF = DE + EF = 13 + 13 = 26