Width of a wall is 4 inches less then the length. The border that surrounds the wall is 2 inches wide and has an area of 240 square inches. What are dimensions

the area of the border is the total area minus the area of the wall. So,

if the width of the wall is w, then since there is border on each side, we need

(w+4)(w+4+4)-w(w+4) = 240
8(w+4) = 240
w=26

The wall is 26x30

let w = width , length = w + 4 ... cross section area = w (w + 4)

width with border = w + (2 * 2) = w + 4

length with border = w + 4 + (2 * 2) = w + 8

area with border = (w + 4) (w + 8)

area of border = [(w + 4) (w + 8)] - [w (w + 4)] = 240

solve for w , then substitute back to find the length

To find the dimensions of the wall, we need to set up equations based on the given information.

Let's assume the length of the wall is "L" inches. According to the given information, the width of the wall is 4 inches less than the length, so the width would be "L - 4" inches.

Now let's calculate the dimensions of the entire area, including both the wall and the border.

The length of the entire area (including the border) would be "L + 2 + 2", since the border is 2 inches wide on each side. This can be simplified to "L + 4" inches.

Similarly, the width of the entire area would be "L - 4 + 2 + 2", which simplifies to "L" inches.

Now we need to find the area of the entire wall, including the border. The area of a rectangle can be calculated as length multiplied by width, so the equation for the area of this entire wall would be:

Area = (L + 4) * L = 240 square inches

To solve this equation, we can multiply out the terms:

L^2 + 4L = 240

Rearranging the equation to simplify further:

L^2 + 4L - 240 = 0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring this equation:

(L + 20)(L - 12) = 0

Setting each factor to zero:

L + 20 = 0 or L - 12 = 0

Solving for L in each case:

L = -20 or L = 12

Since the length cannot be negative, we discard L = -20 and consider L = 12 as our valid solution.

Therefore, the length of the wall is 12 inches.

Using the information that the width of the wall is 4 inches less than the length, we can calculate the width:

Width = Length - 4 = 12 - 4 = 8 inches

So, the dimensions of the wall are 12 inches by 8 inches.