Question

example 3
find the value of the variable and yz if y is between x and z.

1. xy = 11, yz = 4c, xz = 83
2. xy
3. xy = 7a, yz = 5a, xz = 6a + 24
4. xy
5. xy = 5n, yz = 2n, xz = 91
6. xy
7. xy = 11d, yz = 9d − 2, xz = 5d + 28
8. xy
9. xy = 3a − 4, yz = 6a + 2, xz = 5a + 22
10. x
11. xy = 4x, yz = x, and xz = 25
12. x
13. xy = 12, yz = 2x, and xz = 28
14. x

Explanation:

Let's solve problem 10 first:

Step1: Use segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given values: \( 11 + 4c = 83 \)

Step2: Solve for \( c \)

Subtract 11 from both sides: \( 4c = 83 - 11 = 72 \)
Divide both sides by 4: \( c = \frac{72}{4} = 18 \)

Step3: Find \( YZ \)

Substitute \( c = 18 \) into \( YZ = 4c \): \( YZ = 4 \times 18 = 72 \)

Step1: Apply segment addition postulate

\( XY + YZ = XZ \), so \( 7a + 5a = 6a + 24 \)

Step2: Simplify and solve for \( a \)

Combine like terms: \( 12a = 6a + 24 \)
Subtract \( 6a \) from both sides: \( 6a = 24 \)
Divide by 6: \( a = 4 \)

Step3: Calculate \( YZ \)

\( YZ = 5a = 5 \times 4 = 20 \)

Step1: Use segment addition

\( XY + YZ = XZ \) gives \( 5n + 2n = 91 \)

Step2: Solve for \( n \)

Combine terms: \( 7n = 91 \)
Divide by 7: \( n = 13 \)

Step3: Find \( YZ \)

\( YZ = 2n = 2 \times 13 = 26 \)

Answer:

\( c = 18 \), \( YZ = 72 \)

Now problem 12: