A rectangular pool is 10 meters long and 6 meters wide. A path of uniform width is built around the pool. If the area of the path alone is 84 square meters, what is the width of the path?

Jawaban: 2 m

Let width = x. Total area including path = (10+2x)(6+2x). Pool area = 60. Path area = (10+2x)(6+2x) - 60 = 84. So (10+2x)(6+2x)=144. Expand: 60+32x+4x²=144 ⇒ 4x²+32x-84=0 ⇒ x²+8x-21=0 ⇒ (x+11)(x-3)=0, so x=3. But wait, that gives x=3, but option? 2 m? Let's check: If x=2, (14)(10)=140, path area=80, not 84. If x=3, (16)(12)=192, path area=132, not 84. I made a mistake. Let's recalc: (10+2x)(6+2x) - 60 = 84 ⇒ (10+2x)(6+2x)=144. Expand: 60+20x+12x+4x²=144 ⇒ 4x²+32x-84=0 ⇒ divide by 4: x²+8x-21=0. Discriminant 64+84=148, not a perfect square. So my numbers are off. Let's try: If path area i