The surface area of this rectangular object is 78, what is x = ? Algebra & Geometry Practice

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

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  • @bottomlinestl2001
    @bottomlinestl2001 หลายเดือนก่อน

    I just want to say thank you for sharing your knowledge with a 44yr old college student who's been away from math for awhile, this has been and is definitely helpful. 💯

  • @davidellis1929
    @davidellis1929 หลายเดือนก่อน +1

    7x^2+8x-39 can be factored as (7x-13)(x+3). I needed to find two factors of 39, with one multiplied by 7, having a difference of 8. 39=3*13, and 7*3 is indeed 8 more than 13. This is a really cool problem, with fractional measurements yielding an integer surface area.

  • @raya.pawley3563
    @raya.pawley3563 หลายเดือนก่อน +1

    Thank you

  • @santokhsidhuatla7045
    @santokhsidhuatla7045 หลายเดือนก่อน

    2(x+2)3x+2(3x*x)+2(x+2)x
    =6x^2+12x+6x^2+2x^2+4x
    14x^2+16x+78
    7x^2+8x=78/2=39
    7x^2+8x-39=0
    -8+_ (64+4*7*39)^1/2=
    8+34=42/14=3
    X=3Ans

  • @dazartingstall6680
    @dazartingstall6680 หลายเดือนก่อน +3

    2((x(x + 2)) + 3x² + (3x(x + 2))) = 78
    (x(x + 2)) + 3x² + (3x(x + 2)) = 39
    x² + 2x + 3x² + 3x² + 6x = 39
    7x² + 8x = 39
    7x² + 8x − 39 = 0
    {Oh gawd! The nested-brackets horror of the quadratic formula in in-line format!}
    x = (−8 ± √(8² − 4(7 × −39)))/14
    x = (−8 ± √(64 + 1092))/14
    x = (−8 ± 34)/14
    {x = (−8 − 34)/14 = [Who cares? It'll be negative.]}
    x = (−8 + 34)/14
    x = 26/14
    x = 13/7
    x = 1.857 (rounded)

    • @panlomito
      @panlomito หลายเดือนก่อน +1

      You can make it easier if you use the advanced abc-formula: x = xtop -/+ delta = -b / 2a -/+ V(b²-4ac) / 2a
      7x² + 8x - 39 = 0 so a = 7 b = 8 and c = -39 a > 0 so top down parabola
      Discriminant D = b² -4ac = (8)² - 4.(7).(-39) = 64 + 1092 = 1156 positive so 2 solutions for y = f(x) =0
      xtop = -b/2a = -(8) / 2.(7) = - 4/7 and delta = V(D) / 2a = V(1156) / 2.(7) = 34 / 14 = 17/7
      x = xtop -/+ delta so x = - 4/7 MINUS 17/7 = -21/7 = -3 or x = - 4/7 PLUS 17/7 = 13/7
      Or even easier by factorising in (7x-13) . (x+3) = 0

    • @dazartingstall6680
      @dazartingstall6680 หลายเดือนก่อน

      @@panlomito I think I follow that. Thank you.

  • @johnmarchington3146
    @johnmarchington3146 หลายเดือนก่อน +2

    I actually got that result, but thought I was wrong - and I have to admit that checking it looked decidedly complicated!!

    • @dazartingstall6680
      @dazartingstall6680 หลายเดือนก่อน

      Checking it is tedious, but not horrific.
      ((13/7 × 27/7) + (13/7 × 39/7) + (27/7 × 39/7)) × 2

    • @panlomito
      @panlomito หลายเดือนก่อน

      Really? A = 2 . (27.39 + 27.13 + 39.13) / 49 = 2 . (1053 + 351 + 507) / 49 = 2 . 1911 / 49 = 78 units²

  • @panlomito
    @panlomito หลายเดือนก่อน

    L = x+2 W = 3x H = x and A = 2 . (LW + LH + WH) = 78 units²
    LW + LH + WH = (x+2) . 3x + (x+2) . x + 3x . x = 3x² + 6x + x² + 2x + 3x² = 7x² + 8x
    A = 2 . (7x² + 8x) = 14x² +16x = 78 units² so 7x² + 8x - 39 = 0 factorised in (7x - 13) . (x + 3) = 0
    x = 13/7 or x = -3 (with x = -3 declined) so x = 13/7
    Check: L = 13/7 + 2 = 27/7 units W = 39/7 units H = 13/7 units A = 2 . (27.39/49 + 27.13/49 + 39.13/49) = 78 units²

  • @chrisdissanayake6979
    @chrisdissanayake6979 หลายเดือนก่อน

    There are 6 surfaces in the rectangle.
    There are 3 sets of 2 equal surfaces such as:
    1)Two of length = x+2 and width = 3x
    The surface area of these 2 surfaces =
    2[(x+2)3x]= 2[3x^2+6x]=6x^2+12x
    2)Two of length =3x
    and width = x
    The surface area of these 2 surfaces =
    2[(3x)x]= 6x^2
    3)Two of length =x+2
    and width = x
    The surface area of these 2 surfaces=
    2[(x+2)x]=2[x^2+2x]=
    2x^2+4x
    The total surface area of the 6 surfaces =
    6x^+12x+6x^2+2x^2+4x= 14x^2+16x
    It is given that the total surface area to be 78 square units.
    Therefore,
    14x^+16x=78
    Dividing by the common factor of 2,
    7x^2+8x=39
    7x^2+8x-39=0
    Factoring,
    (x+3)(7x-13)=0
    Either x+3=0
    OR
    7x-13=0
    If x+3 =0,
    x = -3 units
    If 7x-13=0,
    7x=13
    x= 13/7= 1 6/7 units
    Since x represents a measurement of the rectangle, it cannot be a negative number.
    Therefore, x = 1 6/7 units

    • @panlomito
      @panlomito หลายเดือนก่อน

      If the unit of the area is "units" as in "78 units" the unit of x must be "SQRT(units)" I suppose...

    • @chrisdissanayake6979
      @chrisdissanayake6979 หลายเดือนก่อน +1

      @
      Yes, I am sorry, that was my mistake.
      Thank you so much for correcting me 🙏🏽
      However, area of the surfaces should be 78 square units and x must be 1 6/7 units.

  • @russelllomando8460
    @russelllomando8460 หลายเดือนก่อน

    wow got 13/7 6 surfaces to add 2 each of: 3X x X (X + 2) x 3X (X + 2) x X
    14X^2 + 16X - 78 = 0 divide by 2 7X^2 + 8X - 39 = 0
    (7X - 13) (X + 3) -3 invalid X = 13/7
    that was fun

  • @hexbinoban6170
    @hexbinoban6170 หลายเดือนก่อน

    6x² + 12x + 2x² + 4x + 6x² = 78
    6x² + 6x² + 2x² + 12x + 4x = 78 ## Gelijksoortige Termen Sorteren En Optellen ##
    14x² + 16x = 78
    (x + 4/7)² = 289/49 ## completing the square
    √(x + 4/7)² = ±√(289/49)
    x + 4/7 = ±17/7
    x = 17/7 - 4/7 = 13/7 ≈ 1.85 ✓
    x = 17/7 + 4/7 = 21/7 = 3
    Let see if it's correct 14x² + 16x = 78 >>> 14(1.85)² + 16(1.85) = 14(3.42) + 16(1.85) ≈ 77.48 ✓

  • @Dr_piFrog
    @Dr_piFrog หลายเดือนก่อน

    13/7 or 1.857

  • @gopherspace8571
    @gopherspace8571 หลายเดือนก่อน +1

    😂 I never had a chance 😂
    🧠👀🤣👍👏🙏💪😎🌎🏆

  • @gillianrolland4305
    @gillianrolland4305 หลายเดือนก่อน +2

    It would have been much easier to factorise.

    • @dazartingstall6680
      @dazartingstall6680 หลายเดือนก่อน

      There are no factors of −39 which sum to 8.

    • @panlomito
      @panlomito หลายเดือนก่อน +3

      @@dazartingstall6680 You mean like (7x-13) . (x + 3) = 0 with -13 . 3 = -39 and 21x - 13x = 8x

    • @dazartingstall6680
      @dazartingstall6680 หลายเดือนก่อน +1

      @@panlomito Having seen both you and another person do that, I went looking for answers. I either never learned or had completely forgotten how to factorise a quadratic where a > 1. My mistaken impression was that it couldn't be done. I'm watching a video that explains it.

    • @panlomito
      @panlomito หลายเดือนก่อน

      @@dazartingstall6680 First you start with (7x + ...) . (x + ...) = 0 because the only way to get 7x² = 7x . x
      Then you determine all the possible factors for 39: 1x39 (39x - 1x no) or 3x13 (13x-7x = 8x bingo)

    • @panlomito
      @panlomito หลายเดือนก่อน

      @@dazartingstall6680 For the equation 7x² + 8x - 39 = 0 it is quite easy to see that you begin with
      ( 7x + a ) . ( x + b ) = 0 while 7x . x = 7x²
      Next we factorise 39 in 39 x 1 (39x -/+ 7.1x = 46x or 32x so not good) or 13 x 3 (13x -/+ 7.3x = - 8x or 34x and we have a winner with 8x so a = -13 or +13 and b = -3 or +3
      To get -39 ab = (-13) . (+3) giving -13x + 7.3x = 8x and that is what we looked for !
      a = -13 and b = +3 or (7x -13) . (x + 3) = 0

  • @mauriziograndi1750
    @mauriziograndi1750 หลายเดือนก่อน

    In a few seconds it appears to be 15x4=60
    3x3=9
    9x2=18
    60+18=78
    X=3
    No writing. But the video calculations are unnecessary scaring for such a small problem.

    • @laurendoe168
      @laurendoe168 หลายเดือนก่อน +2

      Except x does not equal 3. Remember, there are 6 faces.