Question

A gardener uses exactly 500 feet of fencing to completely enclose a rectangular

area in her backyard. If the width of her garden is 50 feet less than the length,
what will be the area of her garden?

Answer 1

Explanation:

Let's start by assigning variables to the dimensions of the rectangular garden.

Let L be the length and W be the width.

From the problem statement, we know that the width is 50 feet less than the length, so we can write:

W = L - 50

We also know that the perimeter of the garden is 500 feet, which means:

2L + 2W = 500

Substituting W with L - 50, we get:

2L + 2(L - 50) = 500

Simplifying this equation, we get:

4L - 100 = 500

Adding 100 to both sides:

4L = 600

Dividing both sides by 4:

L = 150

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

W = L - 50 = 150 - 50 = 100

The area of the garden is:

A = L × W = 150 × 100 = 15,000 square feet.

Therefore, the area of the garden is 15,000 square feet.