Evil Geometry Problem

almost as if it specifically asked for an area value and the legitimacy of the problem wasn't even questioned like it would've been if that was an option in a multiple choice format.

I drew a right triangle and labeled the altitude 6 and the hyp 10 and started solving it algebraically using Pythagoras and similar triangles etc. Got the funny result of a complex number for one of the subsegment lengths. I guess that's what can happen when it's an impossible solution :)

Oddly, I did NOT figure out the specific issue, but I DID get a feeling that something was not correct about it.

Remove "right" in the problem.

Oh. The altitude can't be more than 5.

So we ask wrong questions now to get right answers? This is an abortion

It's not stated that the triangle is on an euclidean plane, therefore I see no error here ( ͡° ͜ʖ ͡°)

If you are familiar with Thales's theorem you will be immediately aware, that a triangle with the given measurements is impssible. If the hypothenuse is 10 the maximum hight is 5 or with hight 6 the hypothenuse must be 12 or it is no right triangle.

You can use the concept of similar triangle which would yield us the equation
36=x * (10-x)
Which has 2 complex roots
So we can conclude there exists no such triangle

In such a right triangle with base = B and height = H, it is necessary and sufficient that B >= 2H (a trick of quadratic equation). With B=10 and H = 6, 10 >= 12 is false. Does not exist.

So.....
In a right angle triangle, the shortest distence between the right angle and the hypotenuse cannot be more than half of the length of the hypotensue.
Is this right?

Ah, yeah 6>5 good math.

No problem, I slay evils

Yes

got answer in argand plane 😃

The circle imbeds a completely different if not competing system

You get the point, right and left, it can only be a circle, which can take on a sphere of its own due to its symmetric superiority

First he called it an altitude then he denied it's not an altitude. What an logic!
Man, just use geometric mean theorem to teach your student instead of this illogical thing.

I teach Thales's theorem in my geometry classes, so it’s obvious once I think about it…but I DO NOT pre-test every textbook question. (They’re supposed to be well vetted.) Whoever included what turns out to be a a non-Euclidean “right triangle” in a high school textbook needs to probably go back and reread “Math Textbook Authoring/Publishing For Dummies,” (along with quite a few other folks out there to be fair).

I generally contacted the publishers in such cases, but someone didn’t even bother to construct this (presumably plane) triangle because they were just thinking
A=bh/2, so it’s 30 (which would be their answer).

That is UNLESS the ACTUAL problem set also stated “NOTE: these problems may have no solution, in which case that should be your answer,” which I love, but have only seen on Smarter Balanced tests.

OR ALTERNATIVELY, the author may have envisioned a 6-8-10 right triangle (in which the book answer would have been 24 and the altitude from the hypotenuse actually works out to be 4.8).

Either way, here’s textbook problem set writing/publishing rule #1: have other authors (and ideally many outside teachers and students) try all problems PRIOR to publication. (It’s also a great task for graduate students and math majors.) AS A BONUS, if you really want to be sure all the problems are good, award a cash prize to the first person who finds a bona fide issue.

I believe the text book didn't mean that the hypotenuse is 10. I think the text book meant to say that 10 is the distance between the right point of the triangle to the point where the altitude line meets the hypotenuse.

In that case, it can be calculated that the length of the hypotenuse is 13.6. Therefore, the area of the triangle is 40.8.

I min wait 🫸🏻🫷🏻 what's answer

euclid theorem h^2=pk (10-x)x= 36 which has no real solution

I have read most of the comments and they are justified. You are just messing with our lives. Don't come with your technicals. My advice to you is the next time you visit the toilet don't use toilet paper, use sandpaper😂

This is actually a way to prove that the geometric mean of two numbers is always less than or equal to their arithmetic mean. Fun problem.

What a BS question

I did it by Pythagorean and found roots to be complex
Done by a 10th grader indian 😅😅

I went on trying to calculate it using A^2 + B^2 = 100, (A*B)/2 = Area…

I eventually found out that the triangle doesn’t make sense.

bD

And the highest degree posible for the big angle is roughly 79.6

hypotenuse = x + y = 10
opposite side = sqrt(36+x^2)
adjacent side = sqrt(36+y^2)

[sqrt(36+x^2)]^2 + [sqrt(36+y^2)]^2 = 10^2
x^2 + y^2 = 28

x + y = 10 / ^2
x^2 +2xy + y^2= 100

x^2 + y^2 + 2xy = 100
x^2 + y^2 = 28
2xy = 72

x*y = 36
x+y=10

x, y ∈ R+, x,y ∈ (0; 10) -> x+y=10

There is no such a pair of numbers that satisfy all the conditions therefore it is contradictory which means there is no such a right triangle with given dimensions.

It's a fault from the exam dept😂😂🎉

So, it wasn't a right, but rather a wrong, triangle?

If the altitude divides the hypotenuse into two parts , x and 10-x, applying Pythagoras theorem on the three right triangles gives

6²+x² + 6²+(10-x)² = 10²
→ 2x²-20x+72 = 0
→ x²-10x+36 = 0

If a, b, c are the coefficients, b²≥4ac is required for x to have real values.

As b² = 10²=100 and 4ac = 4×1×36=144, b²<4ac. So x doesn't have any real solutions. Hence the triangle is impossible.

The answer is 304. 304 means HOE. Altitude can't be greater than 5. Wrong question.

Obviously you’re correct that the triangle can’t exist, but not existing has never stopped mathematicians before, hence so many answers involve the square root of minus one

The error is in the question, not the answer.

Yeah, 30 can't be right. Not when put in the context of a circle, with the diameter being the same as hypotenuse of 10. But, got to hand it to the Mindman, though, he tricked me out at first. Coulda sworn the answer was 30.

24

Excellent

Oh shi....

Our math teacher had absolutely no fucks given about non existent triangles in our textbook. The correct answer for her is 30.

Lol I misunderstood the condition and started to calculate the lengths of the legs of the triangle to find that they are impossible given the dimensions posed. Thought I made an error just to unpause the video and learn I accidentally found the real, hidden answer, 😂

Again, this is a question problem. These seem to be very common and it's dissapointing!!!

30 units ² is the answer

Why would the max height not be 4.8? The side lengths of the traingle should be 6-8-10, making the area of the triangle 24. This would make the height of the triangle 4.8?

Fek!

Errors by the education department stresses many students and wastes their time. Punishment is in order.

The altitude may reach only half the hypothenuse because it is the radius of the circle which must fit to the right triangle.

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