Question

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

Answer 1

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