A rectangle retaining wall has area of 15 square feet. The height of the wall is two feet less than its length. find the height and the length of the wall

The wall is 3 ft high and 5 ft long.

Step-by-step explanation:

Recall: Area of the rectangular wall is A = (length) (height).

Let the height be represented by h. Then the length is represented by h + 2.

The formula A = (length) (height) then becomes A = h (h+2) = 15 ft², which, written in the standard form of a quadratic equation, is h² + 2h - 15 = 0.

Let's solve this last equation for h using completing the square:

h² + 2h - 15 = 0 becomes h² + 2h + 1 - 1 - 15 = 0, or (h + 1) ² = 16. Taking the square root of both sides, we get:

h + 1 = ±4, which is equivalent to h = 3 and h = - 5. Discard the negative result. Then h = 3 and w = 3+2 = 5.

The wall is 3 ft high and 5 ft long. Its area is (3 ft) (5 ft) = 15 ft²