If the sides of a triangle have measurements 3x+4, 6x-1, and 8x+2, find all possible values of x.?
551883
The answer is C\nwell, one side's length of a triangle should be shorter than the other 2's plus (2 sides plus should be longer than one side)\nthen: 3x+4+8x+2>6x-1\n      8x+2+6x-1>3x-4\n      6x-1+3x+4>8x+2\n--> x>-7/5\n    x>3/11\n    x>-1\nThus, the answer should be x>3/11\n:)
1074757
The problem is that 30, 31, and 63 are not the sides of a valid triangle.  For any triangle with sides a,b,c, you must have\na + b > c\nb + c > a\nc + a > b\nBut you have a + b < c, so the triangle isn't valid.
217384
you mean if you have two angles?  For angles x,y,z of a triangle:\n\nx + y + z = 180\n\nI'll let you go from there...
1183842
find the are  (base x height = area) and time that by 3........   OR  ........ take each of the length of the sides and times it by 3...
967287
The triangle will have 2 sides of length x, and the remaining side will be length P-2x making the parameter x + x + P - 2x = P.\nBegin by drawing a line from the vertex where the two sides of length x meet, to the center of the side which is length P-2x. The line should be perpendicular to the side P-2x thereby splitting the triangle in half, into 2 right triangles. One of the right triangles has hypotenuse = x and one leg = (1/2)(p-2x). So the remaining leg has length S.R. (x^2 - (p/2 -x)^2). We calculate the area of this right triangle, and double it since there are two triangles:\nArea = (2)(1/2){(1/2)(p-2x)S.R.(x^2 - (p/2-x)^2)\n         = (1/2)(p-2x)S.R.{px - (p^2)/4}\n         = (1/4)(p-2x)S.R.(4px-p^2)\nNote that your given answer is wrong - it has an x^2 where it should have a p^2....
117522
1. x=1.25\nSol'n.\n1/3x+1/2=11/12\n1/3x=11/12-1/2\n1/3x=5/12\nx=15/12\nx=1.25\n\n2. x=-3\nSol'n.\n1.5x+9=4.5\n1.5x=4.5-9\n1.5x=-4.5\nx=-3\n\n3. x=28\nSol'n.\n2(x+2)=3(x-8)\n2x+4=3x-24\n24+4=3x-2x\nx=28\n\n4. x=-12\nSol'n.\nx+5=-7\nx=-7-5\nx=-12\n\n5. x=-10.5\nSol'n.\n-4/7x=6\nx=-42/4\nx=-10.5\n\n6. x=261\nSol'n.\nx/3+2=89\nx/3=89-2\nx/3=87\nx=261\n\n7. a=3.5\nSol'n.\n3a+13=9a-8\n13+8=9a-3a\n21=6a\na=21/6\na=3.5\n\n8. n=0.8\nSol'n.\n15n+9=21\n15n=21-9\n15n=12\nn=12/15\nn=0.8\n\n9. x=-1\nSol'n.\n2(x+6)=-2(x+-4)\n2x+12=-2x+8\n2x+2x=8-12\n4x=-4\nx=-1\n\n10.x=0\nSol'n.\n-(x+2)-2x=-2(x+1)\n-x-2-2x=-2x-2\n-3x+2x=-2+2\n-x=0\nx=0
156289
Yes, follow the suggestion of x60157. In addition, if you can determine the:\n\n1. height ,h, of each triangle you can use the formula for area: A = 0.5bh where b = side prependicular to the height\n\n2. sides of the triangle, then this formula can be used:\nA = Sq. root of (s(s-a)(s-b)(s-c)) where a,b,c are the sides of each triangle; s = semi-perimeter = 0.5(a+b+c)
880763
The coordinates of the vertices of the 3 rectangles, by symmetry, would be of the form, (0, +- 1, +-x), (+-1, +- x, 0), and (+-x, 0, +-1), where x is unknown.  (0,1,x), (0,1,-x), and (1,x,0) forms one equilateral triangle. Therefore we know that 4x^2 = 1+(x-1)^2 +x^2 .  This reduces to x^2 + x -1 = 0.  Solving for x, we have x =  1/2(-1 + sqrt(5)).   From this, we can arrive at the ratio of rectangle sides at 1/2(1 + sqrt(5)), which is the golden ratio.
331507
sorry hunny you need at least 2 side lengths in order for us to help you figure it out... plus once you have that the formula for figuring it out is using the pathagorean theorem! a2+b2=c2 (s = squared) say for instance... the 2 sides of your triangle are 7 and 3inches. 3>2+7>2=c>2\nwhich would turn into 9+49=c>2~~~~~~~ then 58=c>2 then to get c by itself(which is needed) you would take the square root of 58! your hypotenuse would equal 7.6 or rounded, 8!\nnow if you use my steps you should be able to do your problem! I'm a 10th grader in geometry and it's the most lovely subject!
644806
if the triangle is a regular triangle\n\na = (1/2)bh\n\na = (1/2)(6)(6 * sin60)\n\na = (1/2)(6)(3√3)\n\na = 9√3 = 15.588\n\n\nfor a regular polygon, \narea = (n*t^2) / (4*tan(π/n))\n\nwhere n = number of sides & t = length of side
169029
first 4x = 6x-2x\n\nthen answer is:  (x-2)(x+6)
1023518
Use the Law of Sines.\n\nsin A/a = sin B/b\n(sin 36)/24 = sin B/47\nsin B = (47 sin 36)/24\nsin B = 1.151079452\nAt this point you have a problem--it is impossible for the sine of an angle to have a value greater than 1.\n\nSo either you copied the problem wrong, or you are being asked to recognize that a triangle cannot be formed with these dimensions.
942453
From symmetry, you have all the angles\n69 for two, and 180-69= 111 for the other two.\nUse the law of cosines: for triangle abc with opposing angles A,B,C we have the length of the 3rd side c for given a,b from:\n\nc = sqrt(a^2 +b^2 -2abcos(C))\n\nIn your case: a=4, b=6 and C = 69 so\n\nBD = sqrt(36+16-48(cos(69)) = 5.9\n\nFor C = 111 we have:\n\nAC = sqrt(36+16-48(cos(111))= 8.32
859744
(x + 4y)(x - 4y)\nI answered 2 of your questions. Do the rest of the questions yourself.
400659
Well... a slightly advanced method is that you should fist realize that a triangle drawn through these three points will have an area = 0\n\nformula for area of a triangle is:\n        \n| a1 b1 1 |\n| a2 b2 1 |  x 1/2 = A\n| a3 b3 1 |\n\nWhere (a1,b1) ; (a2,b2) and (a3,b3) are the 3 vertices of the triangle.\n{Sorry --- no better way to represent a matrix here...}\n\nor; A = 1/2 [ a1(b2-b3) - b1(a2-a3) + (a2.b3 - a3.b2) ]\n\nHere; A = 0 ; a1=-5; b1=1 : a2=1; b2=p and a3=4; b3=-2\n\ntherefore; 0 = 1/2 [ -5(p+2) - (1-4) + (-2 - 4p)]\nor;        0 = [-5p -10 + 3 -2 -4p]\nor;        0 = -9p -9\nor;       9p = -9\n\n=> p = -1\n\nAnother method would be to find the line through two given points and pass the line through the third point... but that is slightly lengthy.... \n\nIf you have any doubt; feel free to ask me.
712502
You know that the diagonal forms a right triangle with the length and the width. So you can use the Pythagorean Theorem.\nx=width=a\nx+1=length=b\n4=diagonal=c\n(a^2)+(b^2)=(c^2)\n(x^2)+(x+1)^2=(4^2)\n(x^2)+(x^2)+2x+1=16\n2(x^2)+2x+1=16\n2(x^2)+2x-16=0\nIf you use the quadratic formula thing (-b plus or minus, etc.)\nthen you get:\nx=2.2838\nor\nx=-7.5\nBut you know that a dimension cannot be negative, so it must be the first one.\nSo if \nx=2.2828\nthat means that that's the width. If you add one to that, you'll get the length.\nSo, the dimensions are:\n2.2838 x 3.2838
763972
Let there be a right-angled triangle.\nnow, \nwe know that, \n(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 2(4n^3 + 2n+ 2n^2)\n=>(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 8n^3 + 4n+ 4n^2\n=>(2n^2+2n+1)^2=(4n^4 + 4n^2 + 8n^3) + (1 + 4n+ 4n^2)\n=>(2n^2+2n+1)^2=(2n^2 + 2n)^2 + (2n+1)^2\nThis gives solutions\n(3,4,5); (5,12,13); (7,24,25); (9,40,41)........................\nthe above relation is true for all n belonging to natural numbers\nthis way you can find solution for any pair of sides the 3rd side been given.\nput the given side equal to one in equation and find positive n by solving the quadratic and find all the sides.\nEg:If hyputenuse is given as 5\nSolve 2n^2 + 2n + 1= 5\n=>n=1 therefore other sides are 3 and 4\n\nChoose this as best, if correct.