Question

The area of John's rectangular lawn and cement border is 1222 square feet. If the cement border is 2 feet wide, and the length of his lawn is 27 feet less than 3 times the width, what are the dimensions of John's lawn?

Answer 1

To find the dimensions of John's lawn, we can set up an equation based on the given information and solve it using factoring, completing the square, or the quadratic formula. The positive root will give us the width of the lawn, which we can substitute into the equation for the length to find the dimensions.

Step-by-step explanation:

To find the dimensions of John's lawn, we can set up an equation based on the given information.

Let's let the width of the lawn be w.

According to the problem, the length of the lawn is 27 feet less than 3 times the width, so the length of the lawn would be (3w - 27).

The area of the lawn and the border is given as 1222 square feet. We can set up the equation:

1. (w + 4) * ((3w - 27) + 4) = 1222
2. (w + 4) * (3w - 23) = 1222
3. 3w^2 - 23w + 12w - 92 = 1222
4. 3w^2 - 11w - 1314 = 0

We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. The roots of the equation will give us the possible widths of the lawn. We can then substitute the width into the equation for the length to find the dimensions of the lawn.

Note: Since the width cannot be negative, we are only interested in the positive root of the quadratic equation.