ANSWER
Length (x) = 25 feet
EXPLANATION
Given:
Desired Outcome:
Length (x) of the ladder
Solve for Length (x) using Pythagoras Theorem
[tex]\begin{gathered} Hyp^2\text{ = Opp}^2\text{ + Adj}^2 \\ x^2\text{ = \lparen x - 1\rparen}^2\text{ + \lparen x - 18\rparen}^2 \\ x^2\text{ = x}^2\text{ -x -x + 1 - x}^2\text{ - 18x - 18x + 324} \\ x^2\text{ - 38x + 325 = 0} \\ (x\text{ - 25\rparen\lparen x - 13\rparen = 0} \\ x\text{ = 25 or x = 13} \end{gathered}[/tex]
when x = 13
x - 1 = 13 - 1 = 12
x - 18 = 13 - 18 = -5 (length cannot be negative)
when x = 25
x - 1 = 25 - 1 = 24
x - 18 = 25 - 18 = 7
Hence, the length of the ladder is 25 feet.
