Respuesta :
The largest area is found to be 8702.5 [tex]ft^{2}[/tex].
We know that area of rectangle
A = xy ........ (1)
Perimeter of rectangle (given) = 590 ft
Using x and y as two variables ;
5x + 2y = 590
solve yb in term of x
y = -5/2 x + 295......(2)
Now we will get area only in one variable from (1) and (2)
A = x ((-5/2)x + 295)
A = -5/2 [tex]x^{2}[/tex] + 295x
differentiate it with respect gto x
A' = -5x + 295........ (3)
find the critical point to get your minima and maxima value.
Put A' = 0, x = 295/5 = 59
x = 59
then , from (2)
y= (-5/2 × 59) + 295 = 147.5
y = 147.5
again differentiate (3)
A'' = -5 < 0. i.e critical point x = 59 is point of maxima.
So, maximum area = 59 × 147.5
Largest area = 8702.5 [tex]ft^{2}[/tex]
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