Math Problem Statement

A farmer builds three sections of a fence, as shown in the figure, where L = 10.00 m, and gets tired. Walking straight back to where he started, how far d did he have to go?

Solution

This problem involves calculating the straight-line distance dd the farmer needs to walk to return to the starting point after building the fence sections.

From the diagram, we observe that the three sections form a right triangle. The fence sections have lengths:

  • Two sides of length L=10.00 mL = 10.00 \, \text{m},
  • One horizontal side of length L/2=5.00 mL/2 = 5.00 \, \text{m}.

To find the straight-line distance dd, we can use the Pythagorean theorem since the path forms a right triangle:

d=(L)2+(L2)2d = \sqrt{(L)^2 + \left(\frac{L}{2}\right)^2}

Substituting L=10.00 mL = 10.00 \, \text{m}:

= \sqrt{100.00 + 25.00} = \sqrt{125.00}$$ $$d = 11.18 \, \text{m}$$ Thus, the farmer needs to walk $$d = 11.18 \, \text{m}$$. Would you like further details on this? Here are five related questions to explore: 1. How would the value of $$d$$ change if $$L$$ were doubled? 2. Can the Pythagorean theorem be applied to any triangle, or just right triangles? 3. What happens to the value of $$d$$ if the farmer builds only two sections instead of three? 4. How can we verify this result geometrically or experimentally? 5. How would this problem change if the farmer walked along a curved path instead of straight sections? **Tip:** Whenever solving problems involving right triangles, the Pythagorean theorem is a powerful tool to find unknown sides!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem

Formulas

d = sqrt(L^2 + (L/2)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-12

Related Recommendation

Calculate Straight-line Distance using the Pythagorean Theorem

Calculating the Hypotenuse Using Pythagorean Theorem for a Farmer's Fence Problem

Calculate Straight-Line Distance Using the Pythagorean Theorem for a Fence Problem

How Far Will a 45-Foot Ladder Reach After Being Pulled 3 Feet from the Wall? Pythagorean Theorem Solution

Calculating the Ladder Length Using the Pythagorean Theorem