Answer: B
Step 1: Find the length of base
\begin{equation*}
\begin{split}
\text{Area of triangle}& = \frac{1}{2}\times \text{ base} \times \text{ height}\\\\
84 \text{ cm}^2& = \frac{1}{2}\times \text{ base} \times 24 \text{ cm}\\\\
84 & = 12\times \text{ base}\\\\
\text{Base}& = \frac{84}{12}\\\\
\text{Base}& = 7 \text{ cm}\\\\
\end{split}
\end{equation*}
Step 2: Find the length of hypotenuse (c)
\begin{equation*}
\begin{split}
c^2 & = a^2 + b^2\\\\
c^2 &= 7^2 + 24^2\\\\
c^2& = 49 + 576\\\\
c^2& = 625\\\\
c& = \sqrt{625} = 25 \text{ cm}\\\\
\end{split}
\end{equation*}
Step 3: Find the perimeter of triangle
\begin{equation*}
\begin{split}
\text{Perimeter}& = a + b + c\\\\
\text{Perimeter}& = 7 + 24 + 25 = 56\text{ cm}\\\\
\end{split}
\end{equation*}
