Question

The length of a rectangular vegetable garden is 4 feet more than its width. After a 2 foot cement border is placed around the garden, the area of the garden and border is 320 square feet. Find the original width and length of the vegetable garden.

Answer 1

Let's assume the width of the rectangular vegetable garden is "w" feet.

According to the given information, the length of the garden is 4 feet more than its width, so the length can be represented as "w + 4" feet.

After a 2-foot cement border is placed around the garden, the new dimensions of the garden (including the border) will be: Width: w + 2 feet Length: (w + 4) + 2 = w + 6 feet

The area of the garden and border is given as 320 square feet:

Area of the garden and border = (Width + 2) * (Length + 2) = 320

Substitute the values we found: (w + 2) * (w + 6) = 320

Now, let's solve for "w" (the original width of the vegetable garden):

w^2 + 8w + 12 = 320

w^2 + 8w - 308 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring, we get:

(w - 14) * (w + 22) = 0

Setting each factor to zero and solving for "w," we get two possible solutions:

1. w - 14 = 0 --> w = 14 feet (width cannot be negative, so this is the valid solution)

Now that we have the width, we can find the length:

Length = w + 4 = 14 + 4 = 18 feet

So, the original width of the vegetable garden was 14 feet, and the original length was 18 feet.