Calculate the Second Base Length: Trapezoid with 300% Perimeter Ratio

To solve this problem, we'll follow these steps:

• Step 1: Calculate the total perimeter as 300% of the known base $17$.
• Step 2: Use the perimeter formula to isolate the unknown base.
• Step 3: Solve for the unknown base.

Now, let's work through each step:
Step 1: Given that the base $17$ is part of the perimeter calculation and that the perimeter is 300% of this base, we have: $P = 3 \times 17 = 51$

Step 2: Using the perimeter formula for a trapezoid $P = a + b + c + d$, where $a = 17$, $c = 8$, $d = 12$, and $b$ is the unknown base, we have: $51 = 17 + 8 + 12 + b$

Step 3: Solve for the unknown base $b$: $51 = 37 + b$ $b = 51 - 37$ $b = 14$

Therefore, the length of the second base of the trapezoid is $14$.