Final answer:
The length of the tank is represented by the expression L = (360x + 495) / (8x + 11), which is already in its simplest form. To find the amount of rubber stripping needed, calculate the perimeter using P = 2L + 2W, with the given expressions for L and W.
Step-by-step explanation:
To find the length of the tank, we use the given area of the top of the tank and the width. Given the area A = 360x + 495 square feet and the width W = 8x + 11 feet, we use the formula for the area of a rectangle, A = length (L) × width (W), to solve for L.
The expression for the length is thus L = A/W = (360x + 495) / (8x + 11). Simplifying, we divide each term in the numerator by the denominator: L = ((360x / (8x + 11)) + (495 / (8x + 11))). Since 360x and 495 do not have common factors with 8x+11, the expression is already in simplest form.
To determine the amount of rubber stripping needed, we have to calculate the perimeter P of the tank's top. The perimeter of a rectangle is given by P = 2L + 2W. Substituting the expressions for L and W we get: P = 2((360x + 495) / (8x + 11)) + 2(8x + 11) = 2(360x + 495 + 16x + 22) / (8x + 11). Simplifying, we find an expression to represent the total rubber stripping required.