A rectangular field is 50 yards wide and 100 yards long. Give the length and width of another rectangular field that has the same perimeter but a smaller area. width \( =\square \) yards length \( =\square \) yards

We start with the original field dimensions: - Width \( w_1 = 50 \) yards - Length \( l_1 = 100 \) yards The perimeter is given by \[ P = 2(w + l) \] For the original field, the perimeter is \[ P = 2(50 + 100) = 2(150) = 300 \text{ yards} \] Any other rectangle with the same perimeter must satisfy \[ 2(w + l) = 300 \quad \Longrightarrow \quad w + l = 150 \] The area of a rectangle is \[ A = w \times l \] The original field has an area \[ A_1 = 50 \times 100 = 5000 \text{ square yards} \] To find another rectangular field with the same perimeter but a smaller area, we can choose any pair \( (w, l) \) such that \[ w + l = 150 \] and \[ w \times l < 5000. \] One possible choice is to let \[ w = 40 \text{ yards}. \] Then \[ l = 150 - 40 = 110 \text{ yards}. \] The area of this new field is \[ A_2 = 40 \times 110 = 4400 \text{ square yards}, \] which is indeed smaller than \( 5000 \) square yards. Thus, one acceptable answer is: - Width \( = 40 \) yards - Length \( = 110 \) yards.