1. **State the problem:** We need to find the length and width of a rectangle where the length is 33 cm less than 4 times the width, and the perimeter is 74 cm. 2. **Write down the formulas and variables:** Let the width be $W$ cm. Length $L = 4W - 33$ Perimeter $P = 2L + 2W$ Given $P = 74$ cm. 3. **Set up the equation using the perimeter formula:** $$74 = 2(4W - 33) + 2W$$ 4. **Simplify the equation:** $$74 = 8W - 66 + 2W$$ $$74 = 10W - 66$$ 5. **Isolate $W$:** $$74 + 66 = 10W$$ $$140 = 10W$$ 6. **Divide both sides by 10:** $$\cancel{10}W = \frac{140}{\cancel{10}}$$ $$W = 14$$ 7. **Find the length $L$ using $L = 4W - 33$:** $$L = 4(14) - 33$$ $$L = 56 - 33$$ $$L = 23$$ **Final answer:** Length is 23 cm. Width is 14 cm.