Question

Pionts D,E and F are collinear with E between D and F. DE=15, Ef=x+17 and DF=3x-10 Find EF and DF

Answer 1

To find the lengths EF and DF, we begin by using the information given about the points D, E, and F being collinear with E between D and F.

We know the following distances:
- \( DE = 15 \)
- \( EF = x + 17 \)
- \( DF = 3x - 10 \)

Since E lies between D and F, we can express the total distance DF as the sum of DE and EF:

\[
DF = DE + EF
\]

Substituting the known values into this equation:

\[
3x - 10 = 15 + (x + 17)
\]

Now let's simplify the right side of the equation:

\[
3x - 10 = 15 + x + 17
\]
\[
3x - 10 = x + 32
\]

Next, we will isolate \(x\) on one side of the equation. Subtract \(x\) from both sides:

\[
3x - x - 10 = 32
\]
\[
2x - 10 = 32
\]

Now, add 10 to both sides:

\[
2x = 42
\]

Then, divide both sides by 2:

\[
x = 21
\]

Now that we have \(x\), we can find the lengths of EF and DF.

First, calculate \(EF\):

\[
EF = x + 17 = 21 + 17 = 38
\]

Now, calculate \(DF\):

\[
DF = 3x - 10 = 3(21) - 10 = 63 - 10 = 53
\]

Thus, the lengths are:

\[
EF = 38 \quad \text{and} \quad DF = 53
\]