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Mathematics 1
Mathematics 1 Deneme Sınavı
Mathematics 1 Deneme Sınavı Sorusu #1254962
Mathematics 1 Deneme Sınavı Sorusu #1254962
Three sides of a rectangular enclosure having one side along a wall must be fenced. Assume that 500 m of fence is available. Find the largest possible area of the enclosure.
7500 m² |
15625 m² |
25000 m² |
31250 m² |
50000 m² |
Yanıt Açıklaması:
Since the perimeter is x + 2y and the total fence available is 500 m we write x + 2y = 500. From this, x is found as,
x=500-2y and the area of this rectengular is x.y=(500-2y).y = 500y-2y²
f(y)=500y-2y²
f'(y)=500-4y
f'(y)=500-4y=0 (for local maximum value)
y=125m and x=250 m
max area is x.y=125m*250m=31250 m²
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