1. **State the problem:** A heptagon has a perimeter of 77 feet. Four sides are equal in length, and the remaining three sides are half as long as those four. We need to find the length of the shorter sides. 2. **Define variables:** Let the length of each of the four equal sides be $x$ feet. 3. **Express the shorter sides:** Each of the three shorter sides is half the length of the longer sides, so each shorter side is $\frac{x}{2}$ feet. 4. **Write the perimeter equation:** The perimeter is the sum of all sides: $$4x + 3 \times \frac{x}{2} = 77$$ 5. **Simplify the equation:** $$4x + \frac{3x}{2} = 77$$ Multiply both sides by 2 to clear the fraction: $$2 \times 4x + 2 \times \frac{3x}{2} = 2 \times 77$$ $$8x + 3x = 154$$ $$11x = 154$$ 6. **Solve for $x$:** $$x = \frac{154}{11} = 14$$ 7. **Find the shorter side length:** $$\text{Shorter side} = \frac{x}{2} = \frac{14}{2} = 7$$ **Answer:** The shorter sides are 7 feet long.