Math Problem Statement

Find FH in the line segment where FG = 53 units and HG = 40 units.

Solution

In the image, we are asked to find the length of segment FHFH. The line segment FGFG is broken into two parts: FHFH and HGHG. We are given the following information:

  • The length of FGFG is 53 units.
  • The length of HGHG is 40 units.

Using this information, we can set up the equation: FH+HG=FGFH + HG = FG Substitute the given values into the equation: FH+40=53FH + 40 = 53

Now, solve for FHFH: FH=5340=13FH = 53 - 40 = 13

Thus, the length of segment FHFH is 13 units.

Do you want more details or have any further questions? Here are some related questions to explore:

  1. If FHFH was unknown but FGFG was smaller, how would that affect FHFH?
  2. Can you explain why we used a linear equation to solve this?
  3. What other geometric problems can be solved using the same reasoning?
  4. How can this type of calculation be applied in real-life contexts?
  5. What happens if the sum of FHFH and HGHG exceeds FGFG?

Tip: In problems with line segments, remember that the total length is always the sum of its parts. This can be generalized to various geometric figures as well!

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Linear Equations

Formulas

FH + HG = FG

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 6-8