1. **State the problem:** We need to find the length and width of a rectangle given that its perimeter is 152 meters and the width is 22 meters less than the length. 2. **Define variables:** Let the length be $L$ meters and the width be $W$ meters. 3. **Express relationship between width and length:** Given $W = L - 22$. 4. **Formula for perimeter:** The perimeter $P$ of a rectangle is given by $$P = 2(L + W)$$ Given $P = 152$, substitute to get $$152 = 2(L + W)$$ 5. **Substitute width in terms of length:** Replace $W$ with $L - 22$ in the perimeter equation: $$152 = 2(L + L - 22)$$ $$152 = 2(2L - 22)$$ $$152 = 4L - 44$$ 6. **Solve for length $L$:** Add 44 to both sides: $$152 + 44 = 4L$$ $$196 = 4L$$ Divide both sides by 4: $$L = \frac{196}{4} = 49$$ 7. **Find width $W$:** Substitute $L = 49$ into $W = L - 22$: $$W = 49 - 22 = 27$$ **Final answer:** Length $L = 49$ meters Width $W = 27$ meters