Solve for Unknown Side Length: Pentagon with Two 8cm Sides and Equal Remaining Sides

Let's solve the problem step-by-step:

• Step 1: Understand that the problem gives us a pentagon with a total perimeter of 31 cm. The sides are structured so that two of them are each 8 cm, and the remaining three sides are equal in length.
• Step 2: Let's define the length of each of the three equal sides as $x$ cm. Therefore, we can express the perimeter of the pentagon as: $2 \times 8 + 3x = 31$.
• Step 3: First, calculate the total length contributed by the two known sides: $2 \times 8 = 16$ cm.
• Step 4: Substitute this into the perimeter equation: $16 + 3x = 31$.
• Step 5: Solve for $x$ by isolating the unknown variable:
  Subtract 16 from both sides: $3x = 31 - 16$.
  Simplify the right-hand side: $3x = 15$.
  Divide both sides by 3: $x = \frac{15}{3} = 5$.

Therefore, each of the three unknown sides has a length of $x = 5$ cm.