A rectangular field has a length of 120 meters and a width of 80 meters. A path of uniform width is built inside the field along its perimeter, reducing the fields area by 1,200 square meters. What is the width of the path? - Imagemakers
A rectangular field has a length of 120 meters and a width of 80 meters. A path of uniform width is built inside the field along its perimeter, reducing the field’s area by 1,200 square meters. What is the width of the path?
A rectangular field has a length of 120 meters and a width of 80 meters. A path of uniform width is built inside the field along its perimeter, reducing the field’s area by 1,200 square meters. What is the width of the path?
This exact question—about a perfectly rectangular field with defined dimensions and a perimeter path profoundly reducing usable space—is not just a math puzzle; it’s a growing topic in modern outdoor design and precision landscaping across the United States. As homes, event spaces, and agricultural initiatives increasingly seek efficient land use, questions about optimizing rectangular acreage often arise—especially when unwanted interior space must be “lost” to create a border path.
The core problem is simple: a 120m × 80m field, total originally 9,600 square meters, sees its area shrink to 8,400 square meters—an exact 1,200 sq m reduction—carried entirely by a uniform-width path running along the inside edge.
Understanding the Context
To find the path’s width—let’s call it x—start by calculating the original area:
120 meters × 80 meters = 9,600 m²
With a path width x running inside along all four sides, the inner rectangle loses length and width equally. The inner dimensions become:
Length = 120 – 2x
Width = 80 – 2x
Image Gallery
Key Insights
Thus, the inner area is:
(120 – 2x)(80 – 2x)
We set up the equation:
Original area – inner area = 1,200
9,600 – (120 – 2x)(80 – 2x) = 1,200
Solving this equation reveals a quadratic that yields a precise, safe solution—ensuring clarity and trust for readers navigating this design decision.
🔗 Related Articles You Might Like:
📰 Clicking Simulators 📰 Clicking This Button 📰 Clickshare App 📰 Inspirational Backgrounds Iphone 📰 How To Turn Off Firewall 📰 Trainerroad 9474616 📰 Coach Handbags Sale 1604175 📰 Pledge Of Allegiance 421353 📰 Boom 2 9065670 📰 The Shocking Trick To Type A Perfect Checkmark Instantly 5447758 📰 Labret Labret Forever The Obsessive Trend You Cant Ignore Anymore 9023058 📰 Sand Tradingview 📰 High Dividend Reits 📰 Amber Riley 5658290 📰 Imessage App 📰 Handbrake Download For Mac 9648190 📰 Realtek 8852Ce Wifi 6E Pci E Nic Driver 📰 4 Star Wars Movie 8025215Final Thoughts
After algebraic simplification, the solution for x emerges as 10 meters—verified through calculation and consistent with practical feasibility.
This number isn’t
