Can you find area of the Purple shaded triangle? | (Right triangles) |

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  • เผยแพร่เมื่อ 30 ต.ค. 2024

ความคิดเห็น • 41

  • @misterenter-iz7rz
    @misterenter-iz7rz 2 วันที่ผ่านมา +2

    Terrific puzzle 🎉.,

    • @PreMath
      @PreMath  2 วันที่ผ่านมา +1

      Glad to hear that!
      Thanks for the feedback ❤️

  • @ناصريناصر-س4ب
    @ناصريناصر-س4ب 2 วันที่ผ่านมา +4

    Let's assume that the area of the triangle AED is x, from which x/(x+14)=AD/AC=ED/BC=14/32, so x=98/9.

  • @santiagoarosam430
    @santiagoarosam430 2 วันที่ผ่านมา +1

    Sobre el triángulo EBC construimos el rectángulo EBCF de área 2*32=64→ Área CFD=32-14=18.
    Si decimos que EB=4→ BC=16 ; ED=7 y DF=9→ Razón de semejanza entre AED y CFD, s=7/9→ s²=49/81→ Área AED=s²*18 =882/81 =98/9 =10,88 cm².
    Gracias y un saludo cordial.

  • @ParamitaBhattacharya
    @ParamitaBhattacharya 2 วันที่ผ่านมา +2

    Please elaborate about the hight of triangle CDE

  • @sadnanjuhib
    @sadnanjuhib วันที่ผ่านมา

    ❤❤

  • @marcelowanderleycorreia8876
    @marcelowanderleycorreia8876 2 วันที่ผ่านมา

    I spent several hours to solve this tricky puzzle... If I was doing a test, I'd never solve this... Congrats professor! 👍

  • @sergioaiex3966
    @sergioaiex3966 วันที่ผ่านมา +1

    Solution:
    Initially, let's dimension the figure:
    AE = a
    ED = n
    EB = b
    BC = m
    Blue Triangle
    A = ½ base × height
    32 = ½ m b
    m = 64/b
    Yellow Triangle
    A = ½ base × height
    14 = ½ n b
    n = 28/b
    The Pink Triangle AED is similar to the Larger Triangle ABC
    The ratio between the areas of similar triangles is equal to the square of the
    similarity ratio. In this case, the bases "n" and "m" are similar
    Area AED = S
    Area ABC = S + 46 (14 + 32)
    Area AED/Area ABC = n²/m²
    S/(S + 46) = (28/b)²/(64/b)²
    S/(S + 46) = (28/b/64/b)²
    S/(S + 46) = (28/64)²
    S/(S + 46) = (7/16)²
    S/(S + 46) = 49/256
    256S = 49S + 2254
    207S = 2254
    S = 2254/207 (÷23)
    S = 98/9 cm² ✅
    S ~= 10,889 cm² ✅

  • @alexundre8745
    @alexundre8745 2 วันที่ผ่านมา +2

    Bom dia Mestre
    Essa eu acertei, fiquei feliz porque estou aprendendo Geometria com o Sr
    Grato

    • @PreMath
      @PreMath  2 วันที่ผ่านมา

      Excelente!
      Fico feliz em ouvir isso!
      Obrigado pelo feedback ❤️

    • @alexundre8745
      @alexundre8745 2 วันที่ผ่านมา

      @@PreMath Muito obrigado pela instrução
      O Sr é um Homem de Bom ❤️

  • @NASIR58able
    @NASIR58able 2 วันที่ผ่านมา

    Very nice

  • @1ClassicalMusicFan
    @1ClassicalMusicFan 2 วันที่ผ่านมา

    Pause at 1:08.
    (I) “The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”
    x/(x+14+32)=x/(x+46)=(AD/AC)^2.
    (2) "If two triangles share a height, then the ratio of their areas is equal to the ratio of their bases." Applying this to △EAD and △ECD, we get
    x/14=AD/CD, or x/(x+14)= AD/AC.
    Combine these 2 results and solve for x to get 18x=196 and x=98/9.

  • @cyruschang1904
    @cyruschang1904 2 วันที่ผ่านมา

    xy = 28
    xz = 64
    y/z = 28/64 = 7/16
    pink triangle is (7/16)^2 = 49/256 of the large triangle
    (14 + 32) cm^2 is 1 - (7/16)^2 = 207/256 of the large triangle
    pink triangle = 46 cm^2 (49/207) = (2254/207) cm^2 = (10 + 184/207) cm^2

  • @quigonkenny
    @quigonkenny 2 วันที่ผ่านมา

    Extend ED up to F, where CF is parallel to EB. As CF and EB are parallel and FE and BC are parallel, and ∠FEB = ∠EBC = 90°, then CFEB is a rectangle. As EC is the diagonal of CFEB, then the area of CFEB is twice the area of ∆EBC, or 2(32) = 64 cm².
    As the area of ∆CDE is 14 and the area of ∆EBC is 32, the area of triangle ∆CFD = 64-(32+14) = 64-46 = 18.
    As ∠CFD = ∠AED = 90° and ∠FDC and ∠EDA are veryical angles and thus congruent, then ∆CFD and ∆AED are similar triangles. As ∆CFD is 18 cm² and ∆CDE is 14 cm², then the ratio of their bases FD to DE is 18/14 = 9/7, as the triangles have the same height.
    As ∆CFD and ∆AED are similar, the ratio of all their sides are the same, so the ratio of their areas equals the square of the ratio of their sides.
    A = (7/9)²18
    A = 49(18)/81 = 98/9 = 10.8​̅ cm²

  • @RayCChoi-nj3gs
    @RayCChoi-nj3gs 2 วันที่ผ่านมา +3

    6:00, why h square over k square? thanks.

    • @ناصريناصر-س4ب
      @ناصريناصر-س4ب 2 วันที่ผ่านมา +1

      Because the ratio of the areas of two similar triangles equals the square of the similarity ratio.

    • @herolivesnu
      @herolivesnu 18 ชั่วโมงที่ผ่านมา

      Please can you prove this theorem you just stated here? I was about asking the same question that he asked. Let's not assert without proofs, please.

    • @herolivesnu
      @herolivesnu 17 ชั่วโมงที่ผ่านมา

      Thanks for stating the theorem. You are absolutely right, I have seen the proof of the theorem. Thank you so much for letting me know that

  • @sergeyvinns931
    @sergeyvinns931 2 วันที่ผ่านมา

    RUSSIA! Рассмотрим трапецию BCDE, её площадь равна (ВС+DЕ)*BE/2=46. BC=BE=8, DE=a; (8+а)*8/2=46; а=7/2;
    АЕ=х; исходя из подобия треугольников AED и ABC, составляем пропорцию 7/2х=8/(8+х), откуда находим х=56/9; теперь находим площадь розового треугольника, А=56*7/9*2*2=98/9.

  • @phungpham1725
    @phungpham1725 2 วันที่ผ่านมา

    It’s tricky but fun😅
    1/ Label the area of the purple area as A
    We have
    1/2 DExEB= 14 (1)
    1/2 BCxEB=32. (2)
    -> (1)/(2)-> DE/BC=14/32=7/16
    The purple triangle and ABC triangle are similar
    so, DE/BC=AE/AB=7/16
    -> A/(A+46) = sq(7/16)=49/256
    -> A=46x49/207= 10.89 sq cm😅😅😅

  • @marcgriselhubert3915
    @marcgriselhubert3915 2 วันที่ผ่านมา

    2.area of EDC = 28 = ED.EB and 2.area of EBC = BC.EB, so by division: ED/BC = 28/64 = 7/16
    Triangles ADE and ACB are similar (same angles), so AE/AB = ED/BC = 7/16. Let's note AE = 7.k and AB = 16.k. Then by difference EB = 9.k
    2.area of AED = AE.ED = 7.k.ED and 2.area of EDC = ED.EB = ED.9.k. So we have area of AED/ area of EDC = 7/9, and as area of EDC = 14, then we have that area of AED = (7/9).(14) = 98/9.

  • @himo3485
    @himo3485 2 วันที่ผ่านมา

    DE*EB/2=14 CB*EB/2=32 DE=28/EB CB=64/EB DE : CB = 7 : 16
    ⊿DEA∞⊿CBA ⊿DEA=7*7*s=49s ⊿CBA=16*16*s=256s
    DECB= 256s-49s=207s=46(cm²) s=2/9
    ⊿DEA=Purple area=49s=49*2/9=98/9(cm²)

  • @georgebliss964
    @georgebliss964 2 วันที่ผ่านมา

    Triangle ABC is not defined uniquely.
    Let EB = BC = 8.
    Comparing blue & yellow triangle areas.
    8 / 32 = DE / 14. ( same heights EB).
    DE = 3.5.
    Similar triangles ABC & AED.
    8 / (AE + 8) = 3.5 / AE.
    Cross multiplying.
    8AE = 3.5AE + 28.
    4.5 AE = 28.
    AE = 28 / 4.5.
    Area of purple triangle.
    1/2 x (28 / 4.5) x 3.5.
    14 x 3.5 / 4.5.
    10.89

  • @PrithwirajSen-nj6qq
    @PrithwirajSen-nj6qq 2 วันที่ผ่านมา

    BC =16x
    DE = 7x
    AE =7 p
    AB= 16p
    BE =( 16-7)p=9p
    Area of 🔺 CBE =
    1/2*BC*BE=1/2 *16x *9p
    = 32 sq units
    xp =32/72=4/9
    Area of 🔺 ADE = 1/2*7x *7p =49xp/2 =49*4/9*2=98/9 sq units

    • @herolivesnu
      @herolivesnu 18 ชั่วโมงที่ผ่านมา

      Nice work, please how did you arrive at values(show formulas), BC? DE? AB? What does x and p mean in your solution?

  • @Kasleyar
    @Kasleyar 2 วันที่ผ่านมา

    Can you teach..... hacsigun into the circle minus or circle into the hacsigun

  • @devondevon4366
    @devondevon4366 วันที่ผ่านมา

    Answer 10.88888 round to 10.89
    Different approach
    Let's label the length of the blue A and the height C
    Let's label the base of the yellow B and the height C (the same height as the blue)
    then BC = 28
    and AC = 64 Equation 1
    B/A = 7/16 (divide BC by AC)
    Hence, B = 7/16 A (multiply both sides by A). This is the base of the purple
    Let's label the base of the purple P
    Since the purple is similar to the large triangle, then
    (P+C)/A = P/7/16 A
    (P+ C) = P/7/16 (multiply both sides by A)
    7/16 P + 7/16 C = P (cross multiply)
    7/16 P + 7/16 C= 16/16 P ( 16/16P = P)
    7/16 C = 9/16 P
    7/16 * 16/9 * C = P
    7/9 C = P This is the height of the purple
    Hence, the base and height of the purple in terms of A and C
    are 7/9 C and 7 /16 A
    Hence, the area of the purple in terms of A and C is
    7/9 C * 7/16 A * 1/2 = 49/144 * 1/2 * AC = 49/ 288 AC
    But recall AC =64 (see equation 1)
    Hence, the area of the purple is 49/288 * 64 = 3136/288
    3136/288 = 10.888888889

  • @ParamitaBhattacharya
    @ParamitaBhattacharya 2 วันที่ผ่านมา

    First comment from Yorkshire UK👍

  • @wasimahmad-t6c
    @wasimahmad-t6c 2 วันที่ผ่านมา

    10 100%raite full area 8×14÷2=56 )(3.4285714286×6÷2=10

  • @andrewlu8959
    @andrewlu8959 19 ชั่วโมงที่ผ่านมา

    x/14=(x+14)/32 => x =98/9

  • @Birol731
    @Birol731 วันที่ผ่านมา

    My way of solution ▶
    A(ΔEBC)= 32 cm²
    A(ΔECD)= 14 cm²
    [EB]= a
    [BC]= b
    [DE]= c
    [AE]= d
    A(ΔEBC)= 32 cm²
    [EB]*[BC]/2
    a*b/2= 32
    ab= 64
    A(ΔECD)= 14 cm²
    [DE]*[EB]/2
    c*a/2= 14
    ca= 28
    Let's divide ab to da :
    ab/ca= 64/28
    b/c= 16/7
    b) ΔAED ~ ΔABC
    [AE]/[AB]= [DE]/[BC]
    d/(d+a)= c/b
    c/b= 7/16

    d/(d+a)= 7/16
    16d= 7d+7a
    9d= 7a
    d= 7a/9
    c) [AB]= a+d
    d= 7a/9
    [AB]= 7a/9 + a
    [AB]= 16a/9
    ab= 64
    (16a/9)*b= s

    s= 64*(16/9)ab/ab
    s= 1024/9
    A(ΔABC)= 1024/9/2
    A(ΔABC)= 1024/18 cm²
    d) Apurple= A(ΔABC) - A(ΔEBC) - A(ΔECD)
    A(ΔEBC)= 32 cm²
    A(ΔECD)= 14 cm²

    Apurple= 1024/18 - 32 - 14
    Apurple= 98/9 cm² ✅

  • @wackojacko3962
    @wackojacko3962 2 วันที่ผ่านมา

    Beginning @ 8:30 , For some odd reason the dimensions of stuff change for me standing on the South Pole or the Equator. Just can't trust myself. Sometimes I'm exact but not so precise. Maybe if I did all my measurements on the 45th Parallel North or South everything would be okay. 🙂

    • @santiagoarosam430
      @santiagoarosam430 2 วันที่ผ่านมา +1

      Aunque más frío, yo me siento más aplomado en el círculo polar ártico.

    • @phungpham1725
      @phungpham1725 2 วันที่ผ่านมา +1

      😊😊😊

  • @nenetstree914
    @nenetstree914 2 วันที่ผ่านมา

    98/9

  • @devondevon4366
    @devondevon4366 วันที่ผ่านมา

    10.88888

  • @LuisdeBritoCamacho
    @LuisdeBritoCamacho วันที่ผ่านมา

    RESOLUTION PROPOSAL :
    01) DE = b(ase)
    02) BC = B(ase)
    03) BE = h(eigth)
    04) Trapezoid [BCDE] Area = (B + b) * (h/2) = 46 ; h*B + h*b = 92
    05) b * h = 28 sq cm
    06) B * h = 64 sq cm
    07) h = 28/b and h = 64/B
    08) 28/b = 64/B ; 28 * B = 64 * b ; 7B = 16b ; b = 7B/16
    09) There are many infinite Solutions for this Equation : b = 7B/16 ; within the Variable Domain D = ]1 ; 14[
    10) Prime Factors of 28 = {2 ; 2 ; 7}
    11) Prime Factors of 64 = {2 ; 2 ; 2 ; 2 ; 2 ; 2}
    12) Then I saw that : 8 * 3,5 = 28. What's the right Solution?
    13) Could it be (Possible Solution) BE = BC = 8 cm? And DE = 3,5 cm? I am not sure!!
    14) Let's try.
    15) 8/(8 + X) = 3,5/X ; 8X = 3,5 * (8 + X) ; 8X = 28 + 3,5X ; 4,5X = 28 ; X = 56/9
    16) 2 * Purple Area = 35/10 * 36/9 = 1.260 / 90 = 126 / 9 = 14
    17) PA = 14 / 2 ; PA = 7 Square Centimeters.

  • @wasimahmad-t6c
    @wasimahmad-t6c 2 วันที่ผ่านมา

    Do you to mee in the area math wanli 20%

  • @Christopher-e7o
    @Christopher-e7o วันที่ผ่านมา

    Pagrium