1. **State the problem:** We have a rectangular land with perimeter 170 m, length 15 m more than width, divided into three parts P, Q, and R. We need to find the area of the largest part. 2. **Define variables:** Let width = $w$ meters. Length = $l = w + 15$ meters. 3. **Use perimeter formula:** Perimeter $P = 2(l + w) = 170$ Substitute $l$: $$2(w + 15 + w) = 170$$ Simplify: $$2(2w + 15) = 170$$ $$4w + 30 = 170$$ $$4w = 140$$ $$w = 35$$ meters. 4. **Find length:** $$l = w + 15 = 35 + 15 = 50$$ meters. 5. **Calculate total area:** $$A = l \times w = 50 \times 35 = 1750$$ square meters. 6. **Analyze the division:** The rectangle is divided by a diagonal from bottom-left to top-right, creating two triangles: one is triangle P, the other is further divided into Q and R. 7. **Area of triangle P:** Since the diagonal divides the rectangle into two equal-area triangles, $$A_P = \frac{1}{2} \times 1750 = 875$$ square meters. 8. **Triangle Q and R:** The right triangle (half the rectangle) is divided by a line parallel to the diagonal, creating Q and R. Since the problem states three parts P, Q, and R, and Q and R are parts of the other half, the largest part is either P or the larger of Q and R. 9. **Without exact dimensions for Q and R, the largest part is triangle P with area 875 square meters.** **Final answer:** The largest part has area **875** square meters.