For over 2000 years the proportions of a “golden rectangle” have been considered visually appealing. A rectangle of width "w" and length "L" is considered “golden” if:\nw/L =L/w+L\n\n\nThe final answer should show L and w to the power of 1
207310
To solve this, first cross multiply the fractions:\n\nW/L = L(W+L)\n\nL^2 = W^2 + WL\nL^2 -WL -W^2 = 0\n\nNow, you can use the quadradic formula, with L as the variable:\n\n[W +or- sqrt(W^2-4(L)(-W))]/(2*1) = L\n\nL = [W +or-sqrt(5W^2]/2\n  = (1/2 +5^(1/2))/2)W  (discard the negative answer, there are no negative lengths)\nL = aprox 1.618 W  which is the golden ratio!
25632
The question is WRONG. If you have length =6 and width =7, P=26 and A=42.
387575
p= 2L + 2 W \n2w=p-2l\nw=(p-2l)/2
442298
Start from basic figures the rectangle. The mid line of the rectangle is parellel to the bases and it is equal to 2* Length/2 = length if the mid line is parellel to is lengthy base. And if the mid line is parellel to breadth then it is equal to 2*Breadth/2= Breadth\nSymbolically,the lengthof the mid line= 2*L/2=L or2*B/2=B\nWhen the breadth line or length line of the rectangle is inclined we call it trapezoid. Please note here that even though sides are inclined position of mid line remains unaltered but the length of the line changes w.r.t. the change in inclination. I think this is enough to prove that the mid line of a trapezoid is always parellel to its bases.\nFurther, as the sides of the rectangle inclines to form a trapezium the it cut out two troangles on either sides of the rectangle. Also it cut out the mid lines. This cut out mid lines will be the mid lines of the triangles that are cut out. If a and b are the lengths of the cut out mid lines then the bases of such triangles that is parellel to its mid line is = 2a and 2b.\nWe know that length or breadth of a rectangle is L or B \nAccordingly, Total length of the bases of the trapesium =  (2L-2a-2b)  or (2B-2a-2b)\n=2(L-a-b)  ; Here L-a-b = D which is the mid line of the trapezoid \nie = 2D\n Threfore length of the mid line of the trapezoid is D which is half of 2D that is the sum of the bases of the trapezoid \nThus proved.\n----------------------------------------------
481319
If L = Length\nW = width\nPerimeter = P = L + L + W + W\nP = 2L + 2W ... (1)\n\nBut in this question \nL - 5 = 3W\nL = 3W + 5 ... (2)\n\nSubstitute this value of L in (1)\nP = 2(3W + 5) + 2W\n\nP = 46\n46 = 2(3W + 5) + 2W\n46 = 6W + 10 + 2W\n46 - 10 = 6W + 2W\n36 = 8W\nW = 36/8\nW = 4.5 cm\n\nSubstitute this value of W in (2)\nL = 3W + 5\nL = 3(4.5) + 5\nL = 13.5 + 5\nL = 18.5cm\n\nCheck ...1\nP = 2L + 2W\n46 = 2(18.5) + 2(4.5)\n46 = 37 + 9\n46 = 46!\n\nCheck ... 2\nL - 5 = 3W\n18.5 - 5 = 3(4.5)\n13.5 = 13.5!
583515
This is a very standard problem. Since it is impossibe to type this in text, I provide the following link to the solution from the Math World Web site:\nhttp://mathworld.wolfram.com/LegendreDifferentialEquation.html
11526
The Edifier has it right, but darned if I can follow the notation. You really need to see this written out like a textbook to understand what's going on.\n\nClick the link below in "sources" to see the answer hosted at my website www.calculus-help.com. Right now, Yahoo! answers, as far as I can tell, doesn't allow graphics, which makes it tricky to answer ANY math questions.\n\nPlease don't post math answers, guys, if the poster knows the answer but can't get there, and you get something completely different.
555402
Let: L=length, W=width, P=perimeter\n\nL=5+2W\n\nP=2L+2W, P=112\n2L+2W=112\nSubstituting L into the equation, we get:\n\n2(5+2W) +2W = 112\n10 + 4W + 2W = 112\n6W = 112-10\n6W = 102\nW = 17\n\nL = 5+2W\nL = 5+ (2*17)\nL = 39\n\nSo, the dimensions of the frame is 39 x 17 inches.
318964
Let L = length and W = width\nThe difference between the length and the width is 7 translates to\nL-W = 7\nso L = W+7\nP = 22\nP = 2L+2W\n22 = 2(W+7) + 2W\n22 = 2W + 14 + 2W\n22 = 4W + 14\n8 = 4W\nW = 2\nL = W+7 so L = 2+7 = 9\nAnswer: L=9, W=2
656497
Let width = W     and     length = L\nL = 7 + W\n\nPerimeter is two widths plus two lengths, so\n2W + 2(7 + W) = 22\n2W + 14 + 2W = 22\n(subtract 14 from both sides)\n4W = 8\n(divide both sides by 4)\nW = 2\n\nSince L = 7 + W, then\nL = 7 + 2\nL = 9\n\nI can't help with the graphing, as that doesn't make sense to me in this problem.
17429
its simple ... 80*70*60 ... 10*0 = 0 !!\n\nright isnt it ??? :D
559013
Let the breadth of each red rectangle be x\n\nSo, area of red portion = 4x + x(3-x)\n\nSo, area of white portion is (4-x)(3-x)\n\nSo, 4x+x(3-x) = (4-x)(3-x)\nor 4x + 3x -3x^2 = x^2 -7x+12\nor 4x^2-14x+12 = 0\nor 2x^2-7x+6 = 0\nor 2x^2-6x-x+6=0\nor(2x-1)(x-3)=0\n\nx=1/2 or 0.5 foot is the reasonable answer.
391471
im assumuing you mean a rectangle? If it was a square itd be 400, if its a rectangle its 80l-l^2
372111
Wait a minute everybody!\nthose vertical lines,( lyl ) could mean absolute value!!\nHelloooo?\nso the answerSSS could be 9 and -9\nsheesh!
429928
fractions are usually of the same units. Meaning the top and bottom number are of the same type, and are more comonly just numbers. \n\nRatios can be like this but don't need to be. If i have 5 apple and 10 oranges the ratio of apples to oranges is 5/10, but i cannot say i have .5 orangples (you can have .5 apples/oranges though). This is because the top is different then the bottom... it is akin to having y/x. \n\nThis is the answer i think you are looking for, but remember that it is still a fraction -- it is just irreducible. Just remember that sometimes the units of the numbers on top and bottom of the ratio will actually be the same even if we are talking about different things (like area and circum.).
496720
let l be the length and w be the width\n lw=111\n\nbut it has a margin so Area= (l-11cm)(w-4)\ndifferntiate\nbut we have 3 unknowns so we use the first ea lw=111\nl=111/w\n\nA=(111/w-11)(w-4)\n\ndA/dw= (111/w-11)+(w-4)(-111/w^2)=0\n\n111/w-444/w^2= 111/w-11\ncancel 111/w\n-444/w^2=-11\ncrossmultiply\nw^2=-444/-11\nw=6.4 cm\nl=111/6.4=17.3
238561
This equation is used in a few subtle ways.\n\nOne particular equation is x^2 - x - 1 = 0.  The unique positive solution, namely x = 1.61803, is known as the Golden Ratio.  This number seems to come up quite a bit in art and architecture, beginning with the Egyptians and the pyramids, the Greeks and the Parthenon, and Da Vinci and the Mona Lisa.  The Wikipedia link I have below gives much more information.\n\nIn general, you can use the equation a x^2 + b x + c = 0 to create fractal images.  For instance, start with a number x_0, and define a sequence x_0, x_1, x_2, ... by the recursion relation\n\na (x_{n+1})^2 + b x_n + c = 0\n\nThe Wikipedia link I have below gives a nice plot of the x_n = u_n + i v_n as points (u_n, v_n) in the plane when a = 1, b = 1, and c = (4+3 i)/10.