Plot triangle $ABC$ with vertices $A(0, 0)$, $B(3, 4)$, and $C(3, 0)$ on graph paper. Using the origin as the point of dilation, enlarge it by a factor of $2$ (imagine using two rubber bands). Label this new triangle $A^\prime B^\prime C^\prime$.  

1. What are the side lengths of the original triangle, $ΔABC$?

   Hint (a):

   Find $AB$ by using the Pythagorean Theorem. For this triangle, $(AC)^2 + (CB)^2 = (AB)^2$.

2. What are the side lengths of the enlarged triangle, $ΔA'B'C'$?

   Hint (b):

   Find $A'B'$ by using the Pythagorean Theorem.

   Answer (b):

   $A'C' = 6, B'C' = 8, A'B' = 10$

3. Calculate the area and the perimeter of $ΔA'B'C'$.