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Maximum area for a rectangle of a given perimeter is a square so side would be 30m and area 900 sq m
Math behind it:
We have two variables X and Y (width and height)
The perimeter of the rectangle is 120, therefore 2X + 2Y = 120
Now that we have an equation we can get rid of one of the variables like so:
2X + 2Y = 120 => 2Y = 120 - 2X => Y = 60 - X
We want to optimize the area (A), which is X*Y:
A = X * Y => Substitute the Y -> A = X * (60 - X) => A = 60X - X^2
To find the maximum area we'll have to find where the derivative A' zero.
A = 60X - X^2 => Find the derivative -> A' = 60 - 2X
A' = 0 => 60 - 2X = 0 => -2X = -60 => X = 30
Filling in the X to get the Y we get: Y = 60 - X => Y = 60 - 30 => Y = 30
Now that we have the X and the Y we can calculate the maximum area which is:
X * Y => 30 *30 => 900
What else can I help you with?
If you have an area of 100 square meters what is the perimeter?
40 meters.
What is the maximum area in square units of a rectangle with a perimeter of 128 units?
1024
What is the perimeter of a rectangle 8 meters x 3 meters?
A rectangle 8 metres x 3 metres has a perimeter (distance around) of 22 metres. It has an AREA of 24 square metres.
The perimeter of a rectangle is 72m the width of the rectangle is 16m what is the area of the rectangle?
To find the area of a rectangle, you need to know the formula: Area = length x width. Given that the perimeter is 72m and the width is 16m, we can calculate the length by using the formula for perimeter of a rectangle: Perimeter = 2(length + width). Substituting the values we have, 72 = 2(length + 16), which simplifies to length + 16 = 36. Therefore, the length of the rectangle is 20m. Finally, the area of the rectangle is 20m x 16m = 320 square meters.
How do you find the area of a rectangle with a perimeter of 36m?
how do you find the area of a rectangle witha perimeter of 36 in You don't. You need more information For example a 1 x 17 rectangle has a perimeter of 36 and its area is 17. But a 2 x 16 rectangle also has a perimeter of 36 and its area is 32.
What are the dimensions of the rectangle with this perimeter and an area of 8000 squares meters?
what are the dimensions of the rectangle with this perimeter and an area of 8000 square meters
If you have an area of 100 square meters what is the perimeter?
40 meters.
What is the maximum area for a rectangle whose perimeter is 136?
The maximum area for a rectangle of fixed perimeter is that of the square that can be formed with the given perimeter. 136/4 = 34, so that the side of such a square will be 34 and its area 342 = 1156.
What is the maximum area of a rectangle with a perimeter of 130?
130/4 (4 sides to a rectangle)= 32.5 32.5*32.5=1065.25 square meters (because the largest area of a rectangle is always a ^ ^ square). length width
What is the perimeter of a rectangle that's area is 28 meters?
112meters.
What is the maximum area of a rectangle if perimeter is 40 cm?
100 cm2
If you have a rectangle with a perimeter of 12 x 4 meters would it be the same area as a rectangle of 13 x 3 meters perimeter?
No, 12x4 = 48 sq meters. 13x3=39 sq meters.
What is the area if the perimeter of a rectangle is 8 meters?
3 square metres
What is the maximum area in square units of a rectangle with a perimeter of 128 units?
1024
What is the maximum area for a rectangle with a perimeter that is 88?
A square of side 22 has an area of 484. Rectangle 23 x 21 has an area of 483...
What is 8 meters by 4 meters?
You would have a rectangle with surface area of 32m2 and perimeter of 24m.
What is the perimeter and area of a rectangle with a length of 14 meters and a width of 9 meters?
perimeter = 14+14+9+9 = 46 meters area = 14*9 = 126 square meters
