Answer :
The maximum area of a rectangle when given perimeter is simply perimeter/sides.
To get the maximum area, simply divide 160 (perimeter) by 4 (sides in a rectangle) and then square the result:
160/4 = 40
40 x 40 = 1600
The maximum area, when the sides are all of the same length, is 1600 square yards.
Hope this helps!
~ArchimedesEleven
To get the maximum area, simply divide 160 (perimeter) by 4 (sides in a rectangle) and then square the result:
160/4 = 40
40 x 40 = 1600
The maximum area, when the sides are all of the same length, is 1600 square yards.
Hope this helps!
~ArchimedesEleven
Maximum area covered by 160 yards fence will be 1600 square yards.
Let the length and the width of a rectangular region are 'l' and 'w'.
Since, length of a rope covering the rectangular region is 160 yards,
Therefore, length of the rope will represent the perimeter of the rectangular region.
2(l + w) = 160
l + w = 80 ---------(1)
Expression for the area of a rectangular region is,
Area = Length × Width
A = l × w
Substitute the measure of 'w' from equation (1),
w = 80 - l
A = l(80 - l)
A = 80l - l²
For maximum area to be covered, find the derivative of the area with respect to length and equate it to zero.
A'= 80 - 2l
For A' = 0,
80 - 2l = 0
l = 40 yards
By substituting l = 40 in the expression of the area,
Area of the rectangular region = 80(40) - (40)²
= 3200 - 1600
= 1600 square yards
Therefore, maximum region covered by 160 yards fence will be 1600 square yards.
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