If FG = 12x + 17, GH = 6x + 13, and FH = 20x − 8, what is GH

We are given three line segments: \( FG = 12x + 17 \), \( GH = 6x + 13 \), and \( FH = 20x - 8 \). Since \( F \), \( G \), and \( H \) are collinear, the total length \( FH \) should equal the sum of \( FG \) and \( GH \). Therefore, we have the equation:

\[
FH = FG + GH
\]

Substitute the given expressions:

\[
20x - 8 = (12x + 17) + (6x + 13)
\]

Now, simplify the right-hand side:

\[
20x - 8 = 12x + 17 + 6x + 13
\]

\[
20x - 8 = 18x + 30
\]

Next, subtract \( 18x \) from both sides:

\[
2x - 8 = 30
\]

Add 8 to both sides:

\[
2x = 38
\]

Divide by 2:

\[
x = 19
\]

Now that we know \( x = 19 \), we can find \( GH \). Substitute \( x = 19 \) into the expression for \( GH \):

\[
GH = 6x + 13 = 6(19) + 13 = 114 + 13 = 127
\]

Thus, \( GH = 127 \).

Would you like further details, or do you have any questions? 

Here are five related questions for further practice:

1. What is the value of \( FG \) when \( x = 19 \)?
2. How would you check if your solution for \( FH \) matches the given value?
3. Can you solve for \( x \) if the equation for \( FG \) was \( 12x + 15 \) instead of \( 12x + 17 \)?
4. What happens if the length of \( GH \) is expressed as a quadratic function of \( x \)?
5. How do you solve for the intersection point of two linear functions on a coordinate plane?

**Tip:** When solving linear equations, always combine like terms to simplify the problem step by step.

If FG = 12x + 17, GH = 6x + 13, and FH = 20x − 8, what is GH?

Learn how to solve for GH in the equation where FG = 12x + 17, GH = 6x + 13, and FH = 20x − 8. This problem involves algebraic manipulation and applying the collinearity theorem to find the value of GH. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation