Answer:
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
