1. **State the problem:** We have a square with side length $s$ and an equilateral triangle with side length $t$. Their perimeters are equal, and the sum of one side of the square and one side of the triangle is 28 inches. 2. **Write the equations from the problem:** - Perimeter of square: $4s$ - Perimeter of triangle: $3t$ - Equal perimeters: $$4s = 3t$$ - Sum of sides: $$s + t = 28$$ 3. **Express one variable in terms of the other using the perimeter equation:** From $$4s = 3t$$, solve for $t$: $$t = \frac{4s}{3}$$ 4. **Substitute $t$ into the sum equation:** $$s + \frac{4s}{3} = 28$$ 5. **Combine like terms:** $$\frac{3s}{3} + \frac{4s}{3} = 28$$ $$\frac{3s + 4s}{3} = 28$$ $$\frac{7s}{3} = 28$$ 6. **Solve for $s$ by multiplying both sides by 3:** $$\cancel{\frac{7s}{\cancel{3}}} \times 3 = 28 \times 3$$ $$7s = 84$$ 7. **Divide both sides by 7:** $$\frac{\cancel{7}s}{\cancel{7}} = \frac{84}{7}$$ $$s = 12$$ 8. **Find $t$ using $t = \frac{4s}{3}$:** $$t = \frac{4 \times 12}{3} = \frac{48}{3} = 16$$ **Final answer:** - Side length of the square $s = 12$ inches - Side length of the equilateral triangle $t = 16$ inches