Sure, let's solve this step by step:

1. First, calculate the original area of the garden. The area of a rectangle is given by the formula length x width. So, the original area of the garden is 12 meters x 8 meters = 96 square meters.

2. The problem states that the path reduces the garden's area by 20%. So, the area of the garden after the path is built is 80% of the original area. Calculate this by multiplying the original area by 80% (or 0.8). So, the new area is 96 square meters x 0.8 = 76.8 square meters.

3. Now, let's denote the width of the path as 'x'. The path is built along the inside of the garden, so it reduces both the length and the width of the garden by 2x (x on each side). So, the length of the garden after the path is built is 12 meters - 2x, and the width is 8 meters - 2x.

4. The area of the garden after the path is built is also given by the formula length x width. So, the new area is (12 meters - 2x) x (8 meters - 2x) = 76.8 square meters.

5. Now, we have an equation we can solve for 'x': (12 meters - 2x) x (8 meters - 2x) = 76.8 square meters.

6. This equation simplifies to: 96 - 40x + 4x^2 = 76.8. Rearranging terms gives: 4x^2 - 40x + 19.2 = 0.

7. This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve for 'x' using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this case, a = 4, b = -40, and c = 19.2.

8. Plugging these values into the quadratic formula gives: x = [40 ± sqrt((-40)^2 - 4*4*19.2)] / (2*4) = [40 ± sqrt(1600 - 307.2)] / 8 = [40 ± sqrt(1292.8)] / 8.

9. The square root of 1292.8 is approximately 35.96. So, the two possible solutions for 'x' are (40 + 35.96) / 8 = 9.495 meters and (40 - 35.96) / 8 = 0.505 meters.

10. However, 'x' represents the width of the path, and it cannot be greater than the width of the garden (8 meters). So, the only feasible solution is x = 0.505 meters.

So, the width of the path is approximately 0.505 meters.

Question

Sure, let's solve this step by step:

1. First, calculate the original area of the garden. The area of a rectangle is given by the formula length x width. So, the original area of the garden is 12 meters x 8 meters = 96 square meters.

2. The problem states that the path reduces the garden's area by 20%. So, the area of the garden after the path is built is 80% of the original area. Calculate this by multiplying the original area by 80% (or 0.8). So, the new area is 96 square meters x 0.8 = 76.8 square meters.

3. Now, let's denote the width of the path as 'x'. The path is built along the inside of the garden, so it reduces both the length and the width of the garden by 2x (x on each side). So, the length of the garden after the path is built is 12 meters - 2x, and the width is 8 meters - 2x.

4. The area of the garden after the path is built is also given by the formula length x width. So, the new area is (12 meters - 2x) x (8 meters - 2x) = 76.8 square meters.

5. Now, we have an equation we can solve for 'x': (12 meters - 2x) x (8 meters - 2x) = 76.8 square meters.

6. This equation simplifies to: 96 - 40x + 4x^2 = 76.8. Rearranging terms gives: 4x^2 - 40x + 19.2 = 0.

7. This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve for 'x' using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this case, a = 4, b = -40, and c = 19.2.

8. Plugging these values into the quadratic formula gives: x = [40 ± sqrt((-40)^2 - 4*4*19.2)] / (2*4) = [40 ± sqrt(1600 - 307.2)] / 8 = [40 ± sqrt(1292.8)] / 8.

9. The square root of 1292.8 is approximately 35.96. So, the two possible solutions for 'x' are (40 + 35.96) / 8 = 9.495 meters and (40 - 35.96) / 8 = 0.505 meters.

10. However, 'x' represents the width of the path, and it cannot be greater than the width of the garden (8 meters). So, the only feasible solution is x = 0.505 meters.

So, the width of the path is approximately 0.505 meters.

Knowee AI · Accepted Answer