the perimeter of a triangle is 75 ft. the 2nd side is twice as long as the shortest side. the third side is 5 ft. more than four times the shortest side. what are the 3 sides?
128617
You need to translate your word problem into equations. Call your sides a, b, and c. Your relations state:\n\na+b+c=75\nb=2a\nc=5+4a\n\nReplacing b and c in the first line gives:\n\na+2a+5+4a=75 or 7a+5=75 or 7a=70 or a=10\n\nTherefore b=20 and c=45\n\nThis is not a possible triangle though since 20+10<45.\n\nTherefore no such triangle exists.
508155
You have to use the Pythagorean Theorem.  It says the lengths of the two short sides of a right triangle squared, then added together, equal the length of the long side squared.  Picture a triangle on your sheet of graph paper.  One leg goes from point P straight left to 2,4.  The second goes from 2,4 straight down to Q.  The third connects P and Q and is the longest of the three legs.  The length of the first leg is 2.  The length of the second is 5 (or -5 if you like; it doesn't matter since we're fixing to square it).  The lengths squared are 25 and 4.  So the distance between P and Q squared is 29.  The distance is root(29), which is 5.385.  That's your answer.
182792
The height of a triangle is defined as the perpendicular distance from an angle to a side.  Now, since this is a right triangle, and depending on how it is situated, the height could be 10" or 12" if you observe from the two acute angles.  But from the right angle, the height goes from the angle to AC (your hypotenuse).  Finding this one will be tricky but can be done using the Pythagorean Theorem.\n\nIf you drop a height from the right angle to the hypotenuse, it breaks it into two parts.  The length of one part is x (since we don't know and since the height doesn't perfectly bisect the hypotenuse), and the length of the other part is 15.62-x (since the total length is 15.62").  It really doesn't matter which side is x, but for my explanation, I'll use x as the side closer to the leg that is 10".  This height creates two new right triangles, and you can use the Pythagorean Theorem to find out both the height and the missing side x.\n\nOne formula will end up being 10^2 = h^2 + x^2, and the other formula will end up being 12^2 = h^2 + (15.62-x)^2.  You can solve the first equation to find that h^2 = 100 - x^2 and substitute that in to the second equation:\n\n12^2 = h^2 + (15.62-x)^2\n144 = 100 - x^2 + 243.9844 - 31.24x + x^2\n144 = 343.9844 - 31.24x\n-199.9844 = -31.24x\nx = 6.4 (rounded)\n\nKnowing this, we can find that missing height:\nh^2 = 100 - x^2\nh^2 = 100 - (6.4)^2\nh^2 = 100 - 40.98\nh^2 = 59.02\nh = 7.68"\n\nSo it all depends on the specific height you're looking for - it's either 10", 12", or 7.68".\n\nAs for your trough, surface area is the sum of all the areas.  Break your trough into parts that you can find areas of.  If you're just looking for the outer surface area, for example, you have two triangles for the ends and two rectangles for the sides (assuming that it's an open trough).  The area of the triangles is A = 0.5bh, and the area of the rectangle sides is A = bh (b in this case will be a side of the trianlge, 2, and h will be the length of the trough, 16).  So just add up all the surfaces that will comprise your trough and you should have your surface area.  (I'm not sure if you need to include the inside as well, but if so you need 2 triangles and 2 rectangles for the outside, and 2 triangles and 2 rectangles for the inside as well.)
656815
Well, if the perimeter (thats all the way around the outside or all three sides together is 35, then you can add up the three sides and they should equal 35\n\n3x-5 + 2x-3 + 15-x = 35\n\na little algerbracadabra :  3x+2x-x-5-3+15=35\n\nthen  4x=28\nand x=7\n\nso , put 7 back in for x for each of the sides and you get\n3(7)-5=16\n2(7)-3=11\n15-(7)=8\n\ndouble check just to be sure 16+11+8=35\n\nhurrah \nkeep at it\nmath is power
436988
just add the sides -- that is the definition of a perimeter\n\n2x - 5 + 3x + 1 + 4x +2 \n= 9x - 2\n\nhope this helps !!!
375944
That’s because the slope of the triangle with legs 2 and 5 is different from the slope with legs 7 and 3.  Therefore, the “triangle” isn’t a real triangle.  It just looks like one.\nThe triangles are supposed to look like a 5 by 12 triangle.  But the actual area sum of the parts is only 29.5 compared to 30.
614458
use pythagoras theorm,if left hand side is equal to right hand side then it is a right triangle.\n\nsince 8 is the biggest no here that means the length of hypotenues is 8. \n\nlet side 1 be a=4\nlet side 2 be b=4 sqrt(3)\nlet hypotenuese be c=8\n\naccording to pythagoras theorm,\n\n(a)*(a)+(b)*(b)=(c)*(c)\n\nL.H.S\n\n=4*4+4sqrt(3)*4sqrt(3)\n=16+48\n=64\n\nR.H.S\n=8*8\n=64\n\nsince L.H.S=R.H.S\n\ntherefore, it is a right triangle\n\nhope u understand it\nif u hv any prob u can contact me
558462
Assuming you mean a regular hexagon, then with the 30-60-90 relationship, you should get that half the length of a side is 2.\n\nSo, the area of that yellow triangle in the link below is\n.5 * 2 * 2 * sqrt(3) = 2 * sqrt(3)\n\nThere are 12 triangles, so the area is 24 * sqrt (3).
354209
Let x be the length of the shorter leg.\nLet 5 be the length of the longer leg.\nLet 3x be the length of the hypotenuse.\n\nUsing the Pythagorean theorem:\n5² + x² = (3x)²\n\nMultiply out:\n25 + x² = 9x²\n\nSubtract x² from both sides:\n25 = 8x²\n\nDivide both sides by 8:\nx² = 25/8\n\nTake the sqrt of both sides:\nx² = 50/16\nx = 5 sqrt(2) / 4\n\nx ≈ 1.76776695 ft.
489099
Let L be the length\nLet W be the width\nWe know the perimeter is:\n2(L + W) = 300\nSolving for L:\nL + W = 150\nL = 150 - W\n\nNow write a formula for the area:\nArea = L * W\nArea = (150 - W) * W\nArea = -W² + 150W\n\nYou can see this is the formula for a parabola.  I'll simplify things by expressing it in terms of x:\nf(x) = -x² + 150x\n\nBut it isn't in vertex form:\nf(x) = a(x - h) + k\n\nTo get it in that form, first pull out the -1 to get x²:\nf(x) = -1(x² - 150x)\n\nNow take the coefficient on the x term (-150), take half of it (-75) and square it (5625). Add and subtract this:\nf(x) = -1(x² - 150x + 5625 - 5625)\nNow you can write this as a square:\nf(x) = -1[ (x - 75)(x - 75) - 5625)\nSimplify:\nf(x) = -1(x - 75)² + 5625\n\nYou have a downward facing parabola, with a maximum vertex at the point (h, k) or (75, 5625)\n\nSo the maximum is when the width is 75. When you solve for length you get that the length is also 75. So the maximum area for the patio is a square with sides of length 75 feet.  The total area will be 5,625 sq. feet, a maximum.
335381
Let's say w is the width of the rectangle.  Then, the length will be w+5.  We know the perimeter is 58, and we know that the rectangle has two sides of length w, and two sides of length (w+5).  So...\n\n2w + 2(w+5)=58\n2w + 2w + 10 = 58\n4w + 10 = 58\n4w = 58 - 10\nw = (58-10)/4\nw=48/4\nw=12, the width of the rectangle.\n\nSince the length=w+5, the length is 17.
182685
The perimeter might be 14.0625. \n3+4+5+6+7 = 25 and the pentagons are similar. It is just a matter of proportions. \n(the perimeter of given)/ (perimeter you r tryin to find) = (area of given)/ (area given for the second pentagon)\n\nso in numbers it is (25/x)=(48/27) and you just solve for x because the pentagons are similiar.
452124
24.  The perimeter is just the sum of all the sides
561294
Let the width be x ft and the length be y ft.\nSo perimeter is 2x + 2y = 74\nor x+y=37........(1)\n\nCalculating cost of lengths....\n2y*1 = 2y\n\nCalculating cost of widths....\n2x*4.5 = 9x\n\nTotal cost = 2y +9x = 159........(2)\n\nSolving (1) and (2) simultaneously you get x(width) = 12.14 ft and y(length) = 24.86 ft
390058
I get 5:\n\nThe difference in the y coordinates is:\n-5 - (-1)\n= -5 + 1\n= -4\nBut for a length we take the absolute value --> 4\n\nThe difference in the x coordinates is:\n0 - (-3)\n= 0 + 3\n= 3\n\nSo you have two sides of 3 and 4.  The hypotenuse can be found by remembering the special 3-4-5 triangle, or using the Pythagorean theorem.\n\na² + b² = c²\n3² + 4² = c²\n9 + 16 = c²\n25 = c²\nc = sqrt(25)\nc = 5\n\nIn general, the distance is sqrt((Δx)² + (Δy)²) where Δx is the change in x coordinates and Δy is the change in y coordinates.  I think you made a mistake and accidentally got sides of 3 and 2, rather than 3 and 4.
571117
the shorter piece is 2 feet long and the longer one is 6 feet long\n\n8/4 = 2\n\n2*3 = 6 \n\n6 + 2 = 8
17240
the longest side is the one opposite the largest angle.  the shortest side is the one opposite the smallest angle.  an excellent example pertains to right triangle and the formula a^2 + b^2 = c^2  where c is the hypoteneuse and a and b are the two smaller sides.