Final answer:
To solve for the area of the garden, we first determined the width (46 feet) by solving the perimeter equation, then we found the length by adding 4 feet to the width, resulting in 50 feet. With both dimensions, we calculated the area to be 2300 square feet.
Step-by-step explanation:
To find the area of a rectangular garden where the length is 4 feet longer than the width and the perimeter is 192 feet, we use algebra. Let's define the width of the garden as 'w' feet. Therefore, the length will be 'w + 4' feet. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where 'l' is the length and 'w' is the width. Plugging in the known values, we get 192 = 2(w + 4) + 2w.
Simplifying that equation:
- 192 = 2w + 8 + 2w
- 192 = 4w + 8
- 184 = 4w
- w = 46 feet
Now that we have the width, we can find the length: l = w + 4 = 46 + 4 = 50 feet.
The area (A) of a rectangle is given by the formula A = l × w. Therefore, the area of the garden is:
- A = 50 × 46 = 2300 square feet