# Todd has a rectangular garden with an area of 30 square feet. If the garden is 13 feet longer...

## Question:

Todd has a rectangular garden with an area of 30 square feet.

If the garden is 13 feet longer than it is wide, what is the perimeter of the garden (in feet)?

## Rectangular Area:

Area is the amount of space that is covered by a given geometrical figure or object. A rectangle is a two-dimensional figure that has a length and a width. The rectangular area is the area that is covered by the rectangular figure. We calculate the area of a rectangle using the formula {eq}A = l\times w {/eq}.

Let the width of the rectangular garden be {eq}w\, ft {/eq}. If the length is 13ft longer than the width, then the expression for the length is:

• {eq}l = (w + 13)\, ft {/eq}

The rectangular garden has an area of {eq}A = 30\, ft^2 {/eq}. Therefore:

• {eq}30 = w(w + 13) {/eq}
• {eq}30 = w^2 + 13w {/eq}
• {eq}w^2 + 13w - 30 = 0 {/eq}

Solving the quadratic equation by the use of factorization, we have:

• {eq}w^2 + 15w - 2w - 30 = 0 {/eq}
• {eq}w(w + 15) - 2(w + 15) = 0 {/eq}
• {eq}(w - 2)(w + 15) = 0 {/eq}
• {eq}w = 2\, ft,\quad w = -15\, ft {/eq}

Since length cannot be negative, we will consider the positive value of w.

Therefore, the garden measurements are:

• {eq}w = 2\, ft \,\rm and\, l = 2 + 13 = 15\, ft {/eq}.

The perimeter of a rectangle is given by:

• {eq}P = 2(w + l) {/eq}

Thus, the perimeter of the rectangular garden is:

• {eq}P = 2(2 + 15) = \boxed{34\, ft} {/eq} 