Math Problem Statement
Point G is on line segment start overline, F, H, end overlineFH. Given F, H, equals, 4, x, plus, 8, commaFH=4x+8, F, G, equals, x, commaFG=x, and G, H, equals, 5, x, commaGH=5x, determine the numerical length of start overline, G, H, end overline, .GH.
Solution
We are given the following information:
- The total length of segment .
- The length of segment .
- The length of segment .
Since point is on the line segment , we know that:
Substitute the given values into the equation:
Simplify the left-hand side:
Now, subtract from both sides:
Solve for :
Now that we know , substitute this value back into the expression for :
Thus, the numerical length of segment is .
Would you like further details or have any questions?
Here are 5 related questions to expand on this:
- How would you determine the length of using the same method?
- What is the total length of given that ?
- If another point was added between and , how would you calculate the lengths of the new segments?
- Can the same method be applied if is not between and ?
- What happens if the relationship between the segment lengths changes, such as making instead?
Tip: Always check if points lie on the same line or segment to avoid overcomplicating problems involving distances!
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Linear Equations
Formulas
Segment addition formula (FG + GH = FH)
Solving linear equations
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 8-10