A rectangular garden is 12 m long and 8 m wide. A path of uniform width is built around the garden inside its boundary. If the area of the path is 36 m², what is the width of the path?

Jawaban: 1 m

Let width = x. Inner rectangle dimensions: (12−2x) and (8−2x). Path area = 12×8 − (12−2x)(8−2x) = 96 − (96 − 40x + 4x²) = 40x − 4x² = 36. So 4x² − 40x + 36 = 0 → x² − 10x + 9 = 0 → (x−1)(x−9)=0. x=1 or x=9. x=9 is impossible because 2x=18 > 8. So x=1 m.