Answer:
the dimensions are W = 8 ft and L = 14 ft
Explanation:
Use the variables L and W.
Then P = 44 ft = 2L + 2W, and A = 112 ft² = L·W.
Reducing the first equation, we get 22 ft = L + W. Solving for L, we get L = 22 ft - W.
Substituting 22 ft - W for L in the area equation, we obtain:
A = 112 ft² = L · W = (22 ft - W) · W, or 112 ft² = (22 ft)W - W²
Let's write this in standard form for a quadratic:
112 ft² = (22 ft)W - W² ↔ W² - (22 ft) · W + 112 ft² = 0
The coefficients of this quadratic equation are a = 1, b = -22 and c = 112.
The discriminant is thus (-22)² - 4(1)(112), or 484 - 448 = 36.
Thus, the roots are:
-(-22) ± √36
W = ---------------------
2
22 ± 6
= -------------- , so that W = 14 and W = 8.
2
Since L = 22 - W, L could be either 22 - 8 = 14 or 22 - 14 = 8
Thus, the dimensions are W = 8 and L = 14.
Check: Does WL = 8(14) ft = 112 ft²? YES
Does P = 2W + 2L = 2(8 ft) + 2(14 ft) = 44 ft? YES