what is the width and the length of a rectangle for the area as 81 meters?
612325
length = 9\nwidth = 9
698034
a ) you effectively have a perimeter of 180m because 160 plus 20. \n\n so you take 180/4 because it;s retangle.  so your area would be 45 x 45 = 2025 m^2
359093
Square and Rectangle= lenght*height\ntriangle=base*height divided by 2
282503
Let's break the area into many vertical rectangular strips between x=1 and x=2, each strip so narrow that we can assume that the top of the strip is horizontal. Thus each strip will be a very narrow and tall rectangle.\n\nLet's say the number of vertical strips we use is n. The first strip will have its left-hand side at x = 1, the next will have its left-hand side at x = 1 + 1/n, the third will have its left-hand side at x = 1 + 2/n, and in general the kth strip will have its left-hand side at x = 1 + (k-1)/n.\n\nNow, what is the y value at each of these x points? Using f(x)=x² we get, for the kth point,\n\ny = (1 + (k-1)/n)² = 1 + 2(k-1)/n + ((k-1)/n)² \n\nNow the area of each strip is equal to its base times its height. The base of each strip is 1/n. So the area of the kth strip is\n\nA = 1/n * (1 + 2(k-1)/n + ((k-1)/n)²)\n\nNow we have to add the areas of all these strips from k = 1 to k = n and rearrange the terms.\n\n.....k=n\nA = Σ (1/n + 2(k-1)/n² + (k-1)²/n^3)\n.....k=1   \n\n.....k=n\nA = Σ (1/n + (2k - 2)/n² + (k² - 2k + 1)/n^3)\n.....k=1\n\nGiving all fractions the common denominator of n^3,\n\n.....k=n\nA = Σ ((n² + 2kn - 2n + k² - 2k + 1)/n^3)\n.....k=1\n\n.....k=n\nA = Σ ((n² - 2n + 1)/n^3  + (2kn + k² - 2k)/n^3)\n.....k=1\n\nThe first term in the summation sign appears n times in the sum, so we can take it out by multiplying it by n. \n\nSum going from k=1 to k=n:\nA =  (n² - 2n + 1)/n² + Σ (2kn + k² - 2k)/n^3\n\nNow let's clear the parentheses in the summation:\n\nSum going from k=1 to k=n:\nA =  (n² - 2n + 1)/n² + Σ 2k/n² + Σ k²/n^3 - Σ 2k/n^3)\n\nThe first summation contains k=1, 2, 3, ... n, so we use the formula for the sum of the arithmetic series:\n\nS = n(n+1)/2\n\nso the first summation becomes\n\nn(n+1)/n² = (n² + n)/n² = 1 + 1/n\n\nThe last summation also contains k=1, 2, 3, ... n, so we use the same formula for the sum of a series, and we get\n\nn(n+1)/n^3 = (n² + n)/n^3 = 1/n + 1/n²\n\nFor the middle summation, we have to compute the sum of k² for k=1, 2, 3, ... n, or that is the sum of 1, 4, 9, 16, ... n².\n\nThe site\n\nhttp://mathworld.wolfram.com/PowerSum.html\n\ngives the formula for the sum of the squares of a series as\n\nS = (2n^3 + 3n² + n)/6\n\nso the middle summation becomes\n\n1/3 + 1/2n + 1/6n²\n\nNow, we are almost done.\n\nLet's let the number of strips get very large, go to infinity as a limit. Let's see what each term becomes:\n\n(n² - 2n + 1)/n² becomes 1 as n gets very large,\n1 + 1/n becomes 1 as n gets very large,\n1/n + 1/n² becomes 0 as n gets very large, and\n1/3 + 1/2n + 1/6n² becomes 1/3 as n gets very large.\n\nThe area under the curve is 1 + 1 + 1/3, or 7/3.\n\nYou can see why integral calculus was invented. Using integral calculus, this problem can be solved in two steps. The integral of f(x)=x² is x^3/3. Inserting the limits of x=1 and x=2 gives\n\nA = 2^3/3 - 1^3/3 = 7/3
128617
length, width, depth. Time and space
464398
Find the area.\nArea of a rectangle = length*width\n= 15*20\n= 300\n(2/3)(300) = 200\n300-200 = 100 square feet
471423
The area of the rectangle is:\n A of rectangle = L X W = 12 x 8 = 96 sq in\n\nThe area of the triangle is:\nA of triangle = 1/2 (A)(B) = 1/2 (A)(32 in) where A is the altitude to the base B of the triangle.\n\nsince both areas are equal:\n96 sq. in = 1/2(A)(32 in)\n96 sq. in = A (16 in)\nA = (96 sq. in)/16 in\nA = 6 inches
936604
let the equal sides be x\n1/2x^2=area=20 given\nx^2=40\nx=rt40\nusing the pythagoras theorem\nc^2=a^2+b^2\nc=rt(a^2+b^2)\nthird side=rt(40+40)\n=rt80\n=4rt5 cm
745313
Not enough information. If the rectangle is also a square, then the length of each side would be 32/4 = 8 cm. Letting x be the length of one of an arbitrary pair of sides and y represent the length of a side from the other pair, you do know of course that x and y must satisfy the equation 2x + 2y = 32 cm --> x + y = 16 cm. Since you have two unknowns but just one equation, there are uncountably infinite many possibilities for (x, y).
801034
Here's the answer: (I'm assuming the top of the box is counted in the area)---------   x = side of square base, h = height, S = surface area, P = perimeter length\n\nS = 2x^2 + 4xh\n\nP = 8x + 4h ---->  h = (P-8x)/4  Substituting,\n\nS = 2x^2 + 4*x*(P-8x)/4 = Px - 6x^2\n\nFor your particular case where P = 120 cm,\n\nS = (120x - 6x^2) cm^2
957319
Here's what you know:\narea: 131.2 cm^2\nwidth: 8 cm\narea formula: width x length\n\nSo you know width x length = 131.2\nYou know the width, so plug it in to get the solution
83837
The dimensions of the rectangle are 5.5 cm x 16.5 cm\n\nIf the rectangle is 3x longer than it is wide, then there are four units that make up two sides...1 unit width, and 3 units length.  So we have four units (4x) that make up one half of the perimeter.  That means that eight units (8x) will make up the entire perimeter.\n\n8x = 44cm, therefore x = 5.5cm\nWe already said that one side is 3x and the other is 1x, so that gives us dimensions of 5.5cm x 16.5 cm
921006
Area = πab where a and b are the semi-major and semi-minor axis length
327427
Each side would have length sqrt(3), so the area would be 3 m^2.
123707
Let:\n\nL = length of the rectangle\nW = width of the rectangle\nP = perimeter of the rectangle\n\nGiven:\n\nW = x\nL = 2x - 4\nP = 2L + 2W from geometry\n\nSolution:\n\nP = 2L + 2W\n64 = 2[2x - 4] + 2x\n\n2[2x - 4] + 2x = 64\n\n[4x - 8] + 2x = 64\n\n4x - 8 + 2x = 64\n\n4x + 2x = 64 + 8\n\n6x = 72\n\nx  =  72/6\n\nx  =  12 cm.\n\nTherefore:\n\nW = width = x = 12 cm. ANS.\n\nL = length = 2x - 4 = 2(12) - 4 = 24 - 4 = 20 cm. ANS.
844322
Let width = x, length = 2x.\nPerimeter = x + 2x + x + 2x = 240\nSo 6x = 240\nSo x = 40\nSo width is 40, length is 80, so area = 3200 square feet.
191768
r u sure its not 40 m less, if it is here:\nLet w=width\n    w+40=length\nw(w+40)=21^2\nw^2+40w=441\nw^2+40w-441=0\n(w+49)(w-9)=0\nw=-49 or w=9\nthe width is 9 m and the length is 13 m