The diagram depicts a trapezoidal plot of land that Marisa wants to fence. It shows a right trapezoid with the following dimensions:

• One leg is 30 feet (vertical side, G to F).
• The top side (GF) is 24 feet.
• The slanted side (GH) is 31 feet.

The problem asks for the length of segment FH (the bottom side), which forms a right angle with the leg GF.

This is a classic right triangle problem where GF and FH are the legs of the triangle, and GH is the hypotenuse. We can use the Pythagorean Theorem to find the length of FH:

$GH^2 = GF^2 + FH^2$

Given:

• $GH = 31 \text{ feet}$
• $GF = 30 \text{ feet}$

We can solve for $FH$.

Let me calculate that.The length of segment $FH$ is approximately 7.81 feet.

Thus, the correct length of the segment FH, based on the given options, is about 8 feet.

Would you like further clarification or more details?

Here are five related questions for better understanding:

1. What is the significance of the Pythagorean Theorem in real-world applications like fencing?
2. How would the solution change if the slanted side (GH) had a different length?
3. Could you determine the area of the trapezoidal plot?
4. How could you calculate the total perimeter of the trapezoid to determine the fencing required?
5. How would the problem change if the trapezoid was not a right trapezoid?

Tip: For geometric problems involving right triangles, the Pythagorean Theorem is your go-to tool to solve for unknown sides.