First of all, let's recall that the full circumference is
Now, since 30 is one twelfth of 360, a 30° arc will be one twelfth of the whole circumference. So, if you call the arc length A, you have
Since we know the arc length, we can build and solve the following equation:
Answer: If the wall is 300 meters long, the dimensions of the fence with the maximum area will be 300 × 150 = 45000 m²
Step-by-step explanation:
try combinations in a chart
190 × (600-190)/2 = 38950 = 190 × 205 increasing area
200 × (600-200)/2 = 40000 = 200 × 200
220 × (600-220)/2 = 41800 == 220 × 190
240 × (600-240)/2 = 43200 == 240 × 180
260 × (600-260)/2 = 44200 == 260 × 170
280 × (600-280)/2 = 44800 . == 280 × 160
<u>300 × (600-300)/2 = 45000 == 300 × 150</u> Maximum Area
310 × (600-310)/2 = 44950 . == 310 × 145 decreasing area
320 × (600-320)/2 = 44800 . == 320 × 140
All the best!!
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