1. **State the problem:** We have an equilateral triangle \(\triangle GHJ\) with sides \(GH = 5x - 13\), \(HJ = 11x - 61\), and \(GJ = 7x - 29\). Since the triangle is equilateral, all sides are equal. 2. **Write the equations:** Because all sides are equal, set \(GH = HJ\) and \(HJ = GJ\): $$5x - 13 = 11x - 61$$ $$11x - 61 = 7x - 29$$ 3. **Solve the first equation:** $$5x - 13 = 11x - 61$$ Subtract \(5x\) from both sides: $$-13 = 6x - 61$$ Add 61 to both sides: $$48 = 6x$$ Divide both sides by 6: $$x = 8$$ 4. **Check with the second equation:** $$11x - 61 = 7x - 29$$ Substitute \(x = 8\): $$11(8) - 61 = 7(8) - 29$$ $$88 - 61 = 56 - 29$$ $$27 = 27$$ This confirms \(x = 8\) is correct. 5. **Find the length of each side:** Calculate \(GH = 5x - 13 = 5(8) - 13 = 40 - 13 = 27\) Calculate \(HJ = 11x - 61 = 11(8) - 61 = 88 - 61 = 27\) Calculate \(GJ = 7x - 29 = 7(8) - 29 = 56 - 29 = 27\) 6. **Final answer:** $$x = 8$$ $$GH = HJ = GJ = 27$$ All sides measure 27 units.