Question

A landscape contractor wants to make an exposed gravel border of uniform width around a rectangular pool in a garden. The pool is 10 feet long and 6 feet wide. There is enough material to cover 36 square feet. How wide should the border be

Answer 1

Border should be 1 ft wide

Explanation:

The pool is 10 feet long and 6 feet wide.

Now, since the landscape contractor wants to make an exposed gravel border of uniform width. Let the uniform width of the border be x. Thus it means the length is now (10 + 2x) and width is now (6 + 2x).

We are told there is enough material to cover 36 square feet.. Thus;

New area - old area = 36

[(10 + 2x) × (6 + 2x)] - (10 × 60) = 36

4x² + 32x + 60 - 60 = 36

4x² + 32x = 36

Subtract 36 from both sides to get;

4x² + 32x - 36 = 0

Using quadratic formula, we have;

x = -9 or 1

We will pick the positive value as the width can't be negative.

Thus;

x = 1 ft