A rectangular piece of land is 40m long and 25m wide. A path of uniform width and 426 m^2 area sorrounds the land from outside. Find the width of path

Width of the uniform path that surrounds the piece of land = 3 m

Step-by-step explanation:

Let the width of the path that surrounds the piece of land be x.

The situation described is sketched in the attached image to this solution.

The dimension of the Length of the piece of land including the uniform path that surrounds it = (40 + 2x) m

The Breadth of the piece of land including the uniform path that surrounds it = (25 + 2x) m

The area of the piece of land including the uniform path that surrounds it

= (Area of the piece of land) + (Area of the uniform path that surrounds it)

Area of the piece of land = Length × Breadth = 40 × 25 = 1000 m²

Area of the uniform path that surrounds it = 426 m² (Given in the question)

The area of the piece of land including the uniform path that surrounds it = 1000 + 426 = 1426 m²

But the area of the piece of land including the uniform path that surrounds it is also

= (Length of the piece of land including the uniform path that surrounds it) × (Breadth of the piece of land including the uniform path that surrounds it

= (40 + 2x) + (25 + 2x)

= 1000 + 80x + 50x + 4x²

= (4x² + 130x + 1000) m²

Equation these 2 areas

4x² + 130x + 1000 = 1426

4x² + 130x - 426 = 0

Solving the quadratic equation

x = 3 or -35.5

Since the width cannot be negative,

x = 3 m

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