a rectanglar lawn 36m long and 15m wide has a path of a uniform width around it. if the area of path is 910m2 . find the width of the path?

lawn area = 36*15

lawn+path area = (36+2w)(15+2w)
So, to find w, just solve

(36+2w)(15+2w) - 36*15 = 910

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To find the width of the path, we need to subtract the area of the inner rectangle (lawn) from the area of the outer rectangle (path + lawn).

Given:
Length of the lawn = 36m
Width of the lawn = 15m
Area of the path = 910m²

Step 1: Calculate the area of the inner rectangle (lawn):
Area of the lawn = Length × Width
Area of the lawn = 36m × 15m
Area of the lawn = 540m²

Step 2: Calculate the area of the outer rectangle (path + lawn):
Area of the outer rectangle = Area of the path + Area of the lawn
Area of the outer rectangle = 910m² + 540m²
Area of the outer rectangle = 1450m²

Step 3: Find the width of the path:
Let's assume the width of the path as 'x.'

Since the outer rectangle is formed by the lawn and the path, we can calculate the dimensions of the outer rectangle using the length and width of the lawn:

Length of the outer rectangle = Length of the lawn + 2 × width of the path
Width of the outer rectangle = Width of the lawn + 2 × width of the path

Plugging in the values:
36m + 2x = length of the outer rectangle
15m + 2x = width of the outer rectangle

Step 4: Calculate the width of the path:
Area of the outer rectangle = length of the outer rectangle × width of the outer rectangle
1450m² = (36m + 2x) × (15m + 2x)

Simplify the equation:
1450m² = (540m² + 36m × 15m + 72x + 30x + 4x²)
1450m² = (540m² + 540m + 102x + 4x²)

Combine like terms:
0 = 4x² + 102x + (540m² + 540m - 1450m²)

Simplify further and solve the quadratic equation:
4x² + 102x + 540m - 910m² = 0

Use a solver or factorization to find the solutions for 'x.' Once the equation is solved, 'x' will represent the width of the path.

I am not satisfy with this solution. I want the full solution step by step. If u can send me