The dimensions of the coral if the area is maximized will be 50/3 yards by 25yards.
Measurement is a branch of mathematics used in determining the area and volume of an object.
From the question,
Let the length of the two rectangular corrals be x
Let the length of the three fence section be y
Note that the area of the rectangle A = length * width
A = xy .....1
Also, since the rectangular corrals are to be made from 100 yd, then;
3x + 2y = 100 ..... 2
Divide through by 2
3x/2 + 2y/2 = 100/2
1.5x + y = 50
y = 50 - 1.5x .... 3
Substitute equation 3 into 1 to have:
A = x(50-1.5x)
A = 50x - 1.5x²
Since the total area is to b maximized, this means that:
dA/dx = 0
dA/dx = 50 - 3.0x
0 = 50 - 3x
3x = 50
x = 50/3 yards
Substitute the value of x into equation 3:
y = 50 - 1.5x
y = 50 - 1.5(50/3)
y = 50 - 25
y = 25yards
Hence the dimensions of the coral if the area is maximized will be 50/3 yards by 25yards.
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