A triangle has sides 10 and 6 - what could be the missing side? 

Problem 1 The sum of two sides of triangle is greater than the third side. 10 + 6 =16 All the options satisfies the theorem. But all options are not right. Now we have to check with respect to the theorem below . Theorem --- The difference of two sides of a triangle is less than the third side. 10-6=4 Hence option 1/2/3 does not satisfy the theorem. 10-6

How about the shortest distance between two points is a straight line? Anything less than 5 would make that statement fail.

Unbelievably convoluted explanation. 10-6=4, but thats a straight line. So x>4 to form a triangle.

Euclid's theorem states that " the sum of two sides of a triangle is larger than the third side." So 6+x>10, only x=5 satisfies this inequality. It is very simple when one studies basic triangles theorems of Euclid.

Never heard of this before. Not sure when I'd use it but into the back pocket it goes.

I was confused about this, as I generally assume one can't do it if you can't draw it with protractor, compass and ruler. Then I suddenly realised it must be five because if it was four it would be a straight line and any less the ends wouldn't join. A day without maths is like a day without sunshine.

It can only be 5 because 6 + any of the other values is les than or equal to 10 and a triangle would not be formed

Correct option is (d) 5 The sum of any two sides of a triangle is greater than the third side

Very good explanation

I am shocked at the question and comments! Making mockary of Mathanatics . You can't determine third side of triangle if you know other two,except in case of right angle triangle. Mathanatics is not guesswork.

Excellent! Never heard of the rule of Triangle Inequality before. Thanks for making my day.Will definitely teach my kids.

Excellent explanation your method of teaching is really very professional , fantastic and enjoyable this particular problem makes me to understand the concept of triangle inequality which was forgotten long time ago. Highly appreciated. Thanks

Sum of the two sides of a triangle greater than the third side. It is a pirtulate

Sum of any two sides in a triangle is more than the third side.Hence third side must be more than 4. Very simple.

Great perspective(s) on this lesson. I've seen a few of your videos now and they are great at providing that. As with anything, there are multiple ways to come to a conclusion and you always provide some good OE with the solutions provided. Thank you!

Loved this one ❤ Min > 4 and max < 16 4 & 16 are straight lines

None above. It seems that it is rectangled triangle. As per Pythegorus principle Base square + Altitude square=Diagonal squared. Accordingly the answer is 8.

Using the Triangle inequality law the first three creates numbers less than or equal to 10 and since it must greater than 10 d 5 is right

It is very simple 5. Because sum of any two sides of a triangle must be greater than third side. 6+5>11.

I looked at it & saw lines on a football pitch, A to B along the '10' side & A to B also along the '6' & 'x' sides with a little change of direction in the middle. if you ran those two paths, they'd take different amounts of time, so the total distance has to be greater than 10. only one answer makes that right.

d. It's less a solve question and more of a test taking technique one. It DOES require you to think about what a triangle is. And that makes it a good question.

In a triangle the sum of any two sides must be greater than the third side. According to the above theorem 6+x should be greater than 10 Hence x should be 5 as per the given multiple choices

My proof was, let angle opposite x=0, a straight line. X would = 4. As soon as angle opposite x>0 you have a triangle, but x is also going to be > 4. Therefore answer is 5.

In this case it's a little simpler because 6 + x= 10,there isn't two unknowns.The answer is c 4.Some of the other stuff you put on with 3 variables and no way to factor ate a lot harder.Thats what I need to learn more about.

Get to the fuclin explanation- please!

Sum of two sides of triangle is always greater than third side so answer is 5

You can't tell by the drawing the value of x, but you can certainly tell out of the choices which ones it isn't.

8 is another possible answer. 6^2 + 8^2 =10^2. 36+64=100. In fact, this could be a 3-4-5 triangle with the other numbers.

Thank you very much for making me think I was very smart, even if only for a few seconds.

d ) But not the only solution

Your videos are a greT help, thank you so much. What if two of the answ options were greater than 5 ? Thanks

5 since 6 + 5 = 11, which is greater than one of the side 10, the combined length of any of the two sides must be greater than the other side

Thank you

Basic properties of a triangle, to wit: the sum of any two sides of a triangle is always greater than the third side.

Question should be made more challenging by lengthening the '6' line to give the optical illusion - anyone can tell it can only be 5 from the visual.

5. Третья сторона не может быть равна и больше суммы двух сторон. И , не может быть меньше их разности и равна этой разности.

Thank you for that! I'm a little ashamed I never knew that.

5, sum of any two sides is greater than 3rd side in a triangle

A B and C fail to be triangles. X+6 must be greater than 10. Only D satisfies the problem.

In triangel, 6+x always bigger than 10

*Let's break down the answer for those who wish to understand this type of theorem better.* To find the value of 𝑥 in the given triangle, we can use the properties of triangles. Given that the triangle has sides of length 10, 6, and 𝑥, we should check if it forms a right triangle. If it is a right triangle, the Pythagorean theorem will apply: a² + b² = c² If we assume 𝑥 is one of the legs and 10 is the hypotenuse, we should apply the Pythagorean theorem correctly: 10² = 6² + 𝑥 ² 100 = 36 + 𝑥 ² 100 - 36 = 𝑥 ² 64 = 𝑥 ² 𝑥 = √64 𝑥 = 8 Since this result is not one of the given options (2, 3, 4, 5), we'll use another configuration where 𝑥 is not the hypotenuse. Assuming the given triangle is not a right triangle, we will use the triangle inequality theorem: 1. 𝑥 + 6 ≻ 10 2. 𝑥 + 10 ≻ 6 3. 6 + 10 ≻ 𝑥 Solving these inequalities: 1. 𝑥 ≻ 4 2. 𝑥 ≻ -4 (always true for positive 𝑥) 3. 16 ≻ 𝑥 So, 4 ≺ 𝑥 ≺ 16. the only value among the given options that satisfies this range is: 𝑥 = 5 Therefore, the correct value for 𝑥 is 5.

Portulate

got it D 5 sum of 2 sides must be greater than the 3rd thanks for the fun

The sum of 2 sides of a triangle shoul be greater than the 3rd side. So 5.

Simple question

Why not just work it out using the formula? c^2 = a^2 + b^2 -2ab[cosine c] The letters correspond to the sides opposite the vertices

So, why not x=6 or x=7 ....? Why 5 is the unique solution? It must be proved, not becaus it's only proposed as a solution.

4=

Unnecessary extended solution of a very easy math.

It is 5

5

4 is possible with angles = to zero.

Como os desenhos não estão em escala, este tipo de questão fica muito aberto, pois , com certeza podemos ter valores de 1um, até 15 um.

TG I have AutoCAD and a angle finder because that was confusing AF.

Wow, I am fairly proficient and trigonometry, but I have either never learned or heard of the triangle inequality. I did get the answer right. Go figure! Thanks again.

Sum of two side is more than third ... So Answer is 5

4

Surely the answer could also be 8 as it is a multiple of a pythagorean 345 triangle.

To be accurate we have to get at least one angle value.

I presume the next step is to use the Law of Cosines to compute the angles in order to verify all of the lengths are valid.

John the JACKASS who has a special quality, he always makes a mountain of a mole hill

5 correct answer

If you rotate the 10 side or the 6 side, or both, then x has many solutions. Is an incomplete problem

D 5

The wording is poor, because the size of X is related to the angle between the lines (10) and (6). From the figure, the correct answer would be 4

In a triangle the sum of two sides is greater than the third side. 6+5>10 The explanation is two show the mathematical genius?

5.

8

Your explanation is far too complicated.

Missing side is 5 i.e.(6+5)>10

Rotate the 10 side over the left end of the line to the horizontal and you will know x must be larger than 4...

5. 6+x>10

X=5

2

Gee....cant be 2,3 or 4 cos that wd make the shortest dist between 2 points not a straight line.

Geometry is why I became an accountant and not an engineer.

10+6=16>4

5, needed 0.5 sec

asnwer=(c)4 isit

4 by graphic solution

X must be greater than 10 - 6

According to pythagoras theoram the ans is 8

If eight isnt one of the choices (because it's the most obvious answer) then it certainly can NOT be 4 or 5. Has to be either 2 or 3; more than likely 3. (Oops... :( Looks like Mr. RU-vid Math Man got me on this one )

5 6+x should be greater than 10

My answer is 4

Dont need math for this, straight like is 10 so total of the other two must be bigger than 10 and that is 5.

D

If one side is 10 and another side is 6 then the third side has to be more than 4 so 5 is the only possible answer.

Clearly this isn't drawn to scale. But it has to be 5. No other answer works

👏👏

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Confusing

its not draw correctly, on my screen the ten measures 184mm and x measures 59mm

Unnecessary made complicated and lengthy...

A

C

x=3

Solved at the thumbnail, the only viable answer is d) 5. (Technically anything GREATER than 4 but less than 16.) An answer of 4 or 16 would result in the "triangle" jus tbeing a line, given the existing lengths of 10 and 6. Anything smaller than 4 or larger than 16 is impossilble, unless you're in a Lovecraftian, non-Euclidean nightmare world.... 😜

Cor

Question is wrong