ANSWER
[tex]A.3\operatorname{cm}[/tex]EXPLANATION
The area of the rectangle is given as 24 sq cm and the length, x, is given as:
[tex]x^2+5x=24[/tex]To find the length of the rectangle, x, solve the equation by factorization.
That is:
[tex]\begin{gathered} x^2+5x-24=0 \\ x^2+8x-3x-24=0 \\ x(x+8)-3(x+8)=0 \\ (x-3)(x+8)=0 \\ \Rightarrow x=3;x=-8 \end{gathered}[/tex]Since the length of a rectangle cannot be negative, the correct answer is:
[tex]A.3\operatorname{cm}[/tex]