Can you find all the side lengths of the triangle? | (Special Triangle) |

Learn how to find the side lengths in a 30-60-90 special triangle. Important Geometry and Algebra skills are also explained: Perimeter; area of a triangle formula; Trigonometry. Step-by-step tutorial by PreMath.com
Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
Step-by-step tutorial by PreMath.com
• Can you find all the s...
Need help with solving this Math Olympiad Question? You're in the right place!
I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at
/ premath
Can you find all the side lengths of the triangle? | (Special Triangle) |#math #maths | #geometry
Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!
#FindSideLengths #Area #Perimeter #TriangleArea #GeometryMath
#MathOlympiad #IntersectingChordsTheorem #RightTriangle #RightTriangles
#PreMath #PreMath.com #MathOlympics #HowToThinkOutsideTheBox #ThinkOutsideTheBox #HowToThinkOutsideTheBox? #FillInTheBoxes #GeometryMath #Geometry #RightTriangles
#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths #MathOlympiad #HarvardAdmissionQuestion
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #CollegeEntranceExam
#blackpenredpen #MathOlympiadTraining #Olympiad Question #GeometrySkills #GeometryFormulas #Angles #Height #ComplementaryAngles
#MathematicalOlympiad #OlympiadMathematics #CompetitiveExams #CompetitiveExam
How to solve Olympiad Mathematical Question
How to prepare for Math Olympiad
How to Solve Olympiad Question
How to Solve international math olympiad questions
international math olympiad questions and solutions
international math olympiad questions and answers
olympiad mathematics competition
blackpenredpen
math olympics
olympiad exam
olympiad exam sample papers
math olympiad sample questions
math olympiada
British Math Olympiad
olympics math
olympics mathematics
olympics math activities
olympics math competition
Math Olympiad Training
How to win the International Math Olympiad | Po-Shen Loh and Lex Fridman
Po-Shen Loh and Lex Fridman
Number Theory
There is a ridiculously easy way to solve this Olympiad qualifier problem
This U.S. Olympiad Coach Has a Unique Approach to Math
The Map of Mathematics
mathcounts
math at work
Pre Math
Olympiad Mathematics
Two Methods to Solve System of Exponential of Equations
Olympiad Question
Find Area of the Shaded Triangle in a Rectangle
Geometry
Geometry math
Geometry skills
Right triangles
imo
Competitive Exams
Competitive Exam
Calculate the length AB
Pythagorean Theorem
Right triangles
Intersecting Chords Theorem
coolmath
my maths
mathpapa
mymaths
cymath
sumdog
multiplication
ixl math
deltamath
reflex math
math genie
math way
math for fun
Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

[@mehdismaeili3743]

great as always.

[@PreMath]

Glad you think so! Thanks for the feedback ❤️

[@fadetoblah2883]

Strictly speaking, the perimeter and the area cannot be equal because the unit of measurement is different for each : u vs u². But once we get over that little misnomer, the problem is actually quite pleasant.

[@prossvay8744]

(30° ; 60°; 90°) So BC=x AC=x√3; AC=2x area=1/2(x)(x√3) Prerimeter=x+2x+x√3 1/2(x^2.√3)=3x+x√3 x=2√3+2 So BC=2√3+2 ; AC=4√3+4 ; AB=√3(2√3+2)=2√3+6.❤❤❤ Thanks sir.

[@PreMath]

Excellent! You are the best. You are very welcome! Thanks for sharing ❤️

[@user-hs3cd6vi5v]

interesting for me

[@PreMath]

Glad to hear that! Thanks for the feedback ❤️

[@marcelowanderleycorreia8876]

Congratulationn! Basic concepts and a great question!!

[@PreMath]

Glad it was helpful! Thanks for the feedback ❤️

[@jamestalbott4499]

Thank you!

[@PreMath]

You are very welcome! Thanks ❤️

[@AmirgabYT2185]

2(3+√3)≈9,464 2(√3+1)≈5,464 4(√3+1)≈10,93

[@PreMath]

Excellent! Thanks for sharing ❤️

[@unknownidentity2846]

Let's face this challenge: . .. ... .... ..... The triangle ABC is a 30°-60°-90° triangle, so we can conclude: AB = √3*BC AC = 2*BC The area and the perimeter can easily be calculated: Area = Perimeter (1/2)*AB*BC = AB + AC + BC (1/2)*(√3*BC)*BC = √3*BC + 2*BC + BC (√3/2)*BC² = BC*(√3 + 3) Since BC>0, we finally obtain: BC = (√3 + 3)*(2/√3) = 2*(1 + √3) AB = √3*BC = 2√3*(1 + √3) AC = 2*BC = 4*(1 + √3) Best regards from Germany

[@PreMath]

Bravo! Thanks for sharing ❤️

[@calvinmasters6159]

Sin 30= 1/2 So proportion of sides is 1 : 2 : 1.732 Find multiplier to satisfy a + b + c = (a + b)/2 where c=2a k=5.46 Result = 5.46, 9.46, 10.92

[@henrymei4565]

that is impossible for the triangle's area equal to the triangle's perimeter, the area uses square unit but the perimeter is just the length of the triangle, it is unit.

[@grahamdrage1289]

Mmmmmm! a length cannot equal an area

[@montynorth3009]

Short side = X, long side = 2X, hypotenuse = 1.732X. Area = 0.5 *X * 1.732X. Area = 0.8660X*X. Perimeter = X + 2X + 1.732X. Perimeter = 4.732X. Then 0.8660X*X = 4.732X Divide both sides by X. 0.8660X = 4.732. X = 5.464 = short side. Long side = 5.464 * 1.732 = 9.464. Hypotenuse = 5.464 * 2 = 10.928.

[@PreMath]

Excellent! Thanks for sharing ❤️

[@sergeyvinns931]

AB=a, BC=b, AC=2b. a^2=c^2-b^2. a^2=4b^2-b^2. a^2=3b^2, a=b\/3. P=b(\/3+3), А=b^2\/3/2. Р=А, b(\/3+3)=b^2\/3/2. b=2(\/3+1), а=2(\/3+3, с=4(\/3+1). Р=8\/3+12. А=8\/3+12.

[@PreMath]

Thanks for sharing ❤️

[@wackojacko3962]

Church Lady would say "well isn't that special?" 🙂

[@PreMath]

Your comments are always a breath of fresh air. They are very enlightening❤️

[@wackojacko3962]

I love you man! 🙂

[@misterenter-iz7rz]

a,2a, aqrt(3)a, sides of the triangle, and then (sqrt(3)/2)a^2=(3+sqrt*3))a=sqrt(3)(sqrt(3)+1)a, a=2(sqrt(3)+1), therefore the sides are 2(sqrt(3)+1), 4(sqrt(3)+1), 2(3+sqrt(3))😊.

[@PreMath]

Excellent! Thanks for sharing ❤️

[@MrPaulc222]

Yes, I did find another way, but it's a complete headbanger compared to yours LOL. Thanks again.

[@ALEducation-mz1jz]

🥰

[@PreMath]

Thanks ❤️

[@himo3485]

BC=x AB=√3x AC=2x x･√3x/2 = x+√3x+2x √3x^2/2 = 3x+√3x √3x^2 = 6x+2√3x √3x^2-6x-2√3x=0 x(√3x-6-2√3)=0 x>0 , √3x=2√3+6 x=2+2√3 BC=2+2√3 AB=6+2√3 AC=4+4√3

[@PreMath]

Excellent! Thanks for sharing ❤️

[@inyomansetiasa]

Hello

[@PreMath]

Hello dear 🌹

[@maxwellarregui814]

Sres. Premath, reciban un cordial saludo. Gracias por el ejercicio y su procedimiento. Comentándoles: El perímetro es 12 + 8*3^0.5 unidades lineales, el área es 12 + 8*3^0.5 unidades cuadradas, cómo interpreto esto, si las unidades de medida son diferentes ??. Una inquietud más: Si el triángulo rectángulo no es un notable hay forma de dar solución al problema ??? creo que al menos se debería conocer un lado del triángulo ??? Gracias por la atención que se digne en prestarme. Éxitos.

[@PreMath]

Hola querido, estamos hablando de valores numéricos solo para el perímetro y el área. Gracias por los comentarios ❤️

[@maxwellarregui814]

@@PreMath Gracias por su atención, entendido la primera, es muy importante la segunda inquietud, agradecería su comentario. Éxitos

[@44.hoaivu24]

Nếu chỉ cho số đo của 2 góc, mà không cho số đo bất kì cạnh nào thì ko thể có đáp án cụ thể được

[@yvjanard]

AB is 6 BC is 8 AC is 10

[@bobbyheffley4955]

Area and perimeter have the same numerical value.

[@PreMath]

Thanks for the feedback ❤️

[@PrithwirajSen-nj6qq]

May not agree. Give an example Hypotenuse 13 unit Base 5 unit Perpendicular 12 unit It is 13*13=169 12*12+5*5=144+25=169 Hence the lengths are of a rt triangle. Now perimeter =12+5+13=30 units Area =1/2*perpedicular*base =1/2*12*5=30 sq units Hence may not agree to u. Your given problem bears multiple sets of answer. I only have given one. Plz comment if I am wrong

[@PreMath]

Hello dear, we are dealing with a special 30-60-90 triangle. I really appreciate and value your comment. Thanks for the feedback ❤️

[@LuisdeBritoCamacho]

Unfortunately there is only one single answer for a Triangle (30º ; 60º ; 90º)

[@LuisdeBritoCamacho]

Let's do it!! 1) Triangle [ABC] is (30º - 60º - 90º) 2) AB = X ; BC = Y ; AC = Z 3) Prove : (X * Y) / 2 = (X + Y + Z) ; (X * Y ) = 2X + 2Y + 2Z 4) sin(60º) = X / Z ; X = Z * sin(60º) ; X = Z * sqrt(3)/2 ; X = 0,866*Z 5) cos(60º) = Y / Z ; Y = Z * cos(60º) : Y = Z / 2 6) X * Y = (Z*sqrt(3)/2) * (Z/2) ; X * Y = (Z^2 * (sqrt(3) / 4) ; X * Y = 0,433*Z^2 sq un 7) 2 * (X + Y + Z) = 2 * (0,866*Z + (Z/2) + Z) = (Z*sqrt(3)) + Z + 2Z = (Z*sqrt(3)) + 3Z 8) 0,433*Z^2 = 3Z + Z*sqrt(3) 9) 0,433*Z^2 = 3Z + 1,732Z 10) 0,433*Z^2 = 4,7321*Z 11) Z = 10,9286 lin un 12) X = 0,866*Z = 0,866 * 10,9286 = 9,4642 lin un 13) Y = Z / 2 = 10,9286 / 2 = 5,4643 lin un 14) Check. 15) A = X * Y / 2 = 25, 8576 sq un 16) P = 10,9286 + 9,4642 + 5,4643 = 25,8571 lin un 17) Answer : BC = 5,4643 Linear Units; AB = 9,4642 Linear Units ; AC = 10,9286 Linear Units.

[@PreMath]

Thanks for sharing ❤️ Thanks for the feedback ❤️

[@TheIsmat987]

Teacher. No soluation ..there are many similars triangular

[@triplem1812]

What ? 🤔 I found AB = 8 ; BC = 6 ; AC = 10 and so the perimeter 8+6+10 = 24 and the area 8*6/2 = 24 too... No ? Ah, i think i found my error, i dont respect the angles of 30° and 60°

[@PreMath]

No worries. We are all lifelong learners. Thanks for sharing ❤️

[@Law_Abiding_Citizen_ok]

You didn’t tell us the perimeter or area in the end just the side lengths🙄

[@PreMath]

A=P=8√3+12😀

[@quigonkenny]

AB = 2√3 + 6 BC = 2√3 + 2 CA = 4√3 + 4 P = (2√3+6) + (2√3+2) + (4√3+4) P = 8√3 + 12 ✓ A = (2√3+6)(2√3+2)/2 A = (12+4√3+12√3+12)/2 A = (24+16√3)/2 = 8√3 + 12 ✓

[@44.hoaivu24]

Chu vi ko bằng diện tích đc

[@Teamstudy4595]

1$t 🪟 View

[@PreMath]

Thanks dear ❤️ You are the best!