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yKpoI14uk [10]
3 years ago
12

A rectangular plot is enclosed by 200 m of fencing and has an area of A square metres. Show that :

Mathematics
2 answers:
denpristay [2]3 years ago
8 0
Let x be one side and l be the other side of the plot.
Perimeter = 2(x + l)
200 = 2(x + l)
l = 100 - x

Area of this rectangle:
A = (x)(l)
A = x(100 - x)
A = 100x - x²

To find the maximum value of the area, we differentiate with respect to x and equate to 0
dA/dx = 100 - 2x
0 = 100 -2x
x = 50
l = 100 - 50 = 50
This means the area will be maximized when the sides of the rectangle are equal; that is, when it is a square.
Tema [17]3 years ago
5 0
The perimeter of plot is 200 m. Denote sides of plot with x and y.

P=2(x+y)
\\200=2(x+y)
\\100=x+y
\\y=100-x

The area of plot is A=xy

a) A=xy=x(100-x)=100x-x^2

b) The area is maximal for A'=0
A'=(100x-x^2)'=100-2x
100-2x=0
\\100=2x
\\x=50
\\
\\y=100-x
\\y=100-50
\\y=50

The sides of rectangle are x=50 and y=50. Therefore, the area is maximal if the rectangle is a square.
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Please help ;-; what is the answer?
VashaNatasha [74]

Answer:

  5.7

Step-by-step explanation:

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  AD·CD = BD²

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  2(x² +4.5x) = 16

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  2(x +2.25)² = 26.125 . . . . . write as a square

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We want the value of CD, so ...

  CD = 2x +3 = 2(-2.25 +√13.0625) +3

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7 0
3 years ago
Rachel is making a planter box. If her box measures 345 inches long and 543 inches wide, how many inches of board will she needs
dimaraw [331]

Rachel needs 1776 inches of board

<em><u>Solution:</u></em>

Given that, Rachel is making a planter box

Her box measures 345 inches long and 543 inches wide

Length = 345 inches

Width = 543 inches

<em><u>To find: Inches of board she needs</u></em>

So we need to find the perimeter of the board

The board is usually of rectangular shape

<em><u>Perimeter of rectangle is given as:</u></em>

Perimeter = 2(length + width)

Perimeter = 2(345 + 543)

Perimeter = 2(888)

Perimeter = 1776

Thus she needs 1776 inches of board

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4 years ago
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The answer would be 8/18.

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