Answer: width = 8 ft, length = 10 ft
Step-by-step explanation:
Perimeter = 2L + 2w
36 = 2L + 2w
18 = L + w divided everything by 2
18 - L = w subtracted L from both sides
Area (A) = L · w
80 = L(18 - L) substituted w with 18 - L
80 = 18L - L² distributed L into 18 - L
L² - 18L + 80 = 0 subtracted 18L - L² from both sides
(L - 8)(L - 10) = 0 factored quadratic equation
L - 8 = 0 and L - 10 = 0 applied zero product property
L = 8 and L = 10 solved for L
Next, input the L-values into either equation to solve for w
w = 18 - L
w₁ = 18 - 8 w₂ = 18 - 10
= 10 = 8
So, we have 2 solutions: L = 8, w = 10 and L = 10, w = 8
We generally consider the width (w) to be the smaller value
⇒. w = 8, L = 10
