The area of a rectangular rubber coating for a flat roof is 96 square feet. The length of the rectangular frame is 4 feet greater than the width. We need to find the dimensions (length and width) of the frame.

1. Problem Description

The area of a rectangular rubber coating for a flat roof is 96 square feet. The length of the rectangular frame is 4 feet greater than the width. We need to find the dimensions (length and width) of the frame.

2. Solution Steps

Let $w$ be the width of the frame in feet, and let $l$ be the length of the frame in feet.

We are given that the length is 4 feet greater than the width, so we can write:

$l = w + 4$

The area of the rectangle is given by the formula:

$Area = l \times w$

We are given that the area is 96 square feet, so:

$96 = l \times w$

Substitute $l = w + 4$ into the area equation:

$96 = (w + 4)w$

Expand the equation:

$96 = w^2 + 4w$

Rearrange the equation to form a quadratic equation:

$w^2 + 4w - 96 = 0$

Now we need to solve this quadratic equation for $w$. We can factor the quadratic:

$(w - 8)(w + 12) = 0$

The possible values for $w$ are:

$w - 8 = 0 \implies w = 8$

$w + 12 = 0 \implies w = -12$

Since the width must be a positive value, we have $w = 8$ feet.

Now we can find the length using $l = w + 4$:

$l = 8 + 4 = 12$ feet

So, the width is 8 feet and the length is 12 feet.

3. Final Answer

The dimensions of the frame are:

Width: 8 feet

Length: 12 feet