Can You Find the Area of this Triangle | Geometry Challenge!

[ebich]

I've noticed that. Sometimes it's good to have a joke question like this.

[jaggisarma]

Guruji Namasthey.Ha ha ha that was a nice one. You actually tested our knowledge of geometry and trigonometry.Sir, You know, I almost went as far as doing the √s(s-a)(s-b)(s-c).I, then realised that sides a+b > c.Anyway it turned out to be 0 and I realised it.At least I remembered the formula taught at school 40 yrs ago.Thanks guruji.

[spiderjump]

The triangle is a scaled up version Of a smaller triangle with sides 7, 8
And 15 with scale factor of 111.
Use heron formula to find the area of the smaller triangle then scale up by factor of 111 squared……
Hey wait a minute!!!
It is a straight line !!!’

[easy_s]

Another way to calculate the area of a triangle is √(s(s-a)(s-b)(s-c)) with s=p/2=(a+b+c)/2.
s is half of the perimeter p of the triangle, and the perimeter p is the sum of the three sides (a+b+c). To calculate the area you take the square root of s*(s-a)*(s-b)*(s-c).
In this case you get

[RichWoods]

I worked it out algebraically but assumed I'd made a mistake when I got an imaginary solution. My approach could only have worked if the figure was an actual triangle, so I should have double-checked my reasoning and my calculations and worked backward to ensure that the claimed figure was indeed a valid triangle.

OK, that was sneaky, but it was also a valuable lesson about trusting the numbers.

[Waldlaeufer]

I added 777 to 888 and found 1665, which equals the third side. Therefore, the area of the triangle is zero. :)
Thanks, I didn't start any complicated math!

[ronleblanc]

The area of an ellipse is 0 when the focal distance is equal to the length of its major axis, therefore your triangle is an ellipse. Or a cylinder with 0 radius, or a rectangle with 0 height, or maybe a mobius strip having 0 width, or a tesseract that can't find its way back to the fourth dimension.

[ФёдорИКС]

I've forgotten about triangle inequality, but I used cosine rule to prove that this triangle can't exist (because angle btw 777 and 888 will be 180)

[seroujghazarian]

The area of a triangle of side lengths a, b, and c is:

And, here's the thing. 777+888-1665=0. Thus, the area of the "triangle" in question is 0.

[SladeMacGregor]

Awesome PreMath. Thanks for showing this one.

[suniltshegaonkar]

Please answer here:
if you use trigonometric formula, there you can get some answer (of course that is wrong), but why shout it Not yield Zero?
Area: Sq Root/ s(s-a)(s-b)(s-c), where s = a + b +c.

[king_haku]

You could actually use Heron's Formula to solve this. The semiperimeter would be 1665, and by herons formula the area would be which would be the 0.

[drpkmath]

Another interesting geometry question my friend haha good job!!

[JSSTyger]

You got me. I tried way to hard to figure this out.

[wwoods]

Step one: Let's simplify by dividing the side lengths by the common factor, 111. That gives us a triangle with sides, 7-8-15.
Step two: Hmm....

[rssl]

This is a trick question in my opinion since 777+888 isn’t bigger than 1665 it’s equal to it so the triangle shouldn’t exist and it shouldn’t have an area

[mathswan]

777+888=1665 so the vertices are collinear. Therefore, the area = 0

[salimahmad]

The triangle here in this case is not possible, as the sum of two sides is equal to the third one.

[rssl]

This is noticeable if you plug in the Heron’s formula you will get the area is 0 henceforth this toenails shouldn’t exist

[mokshithreddy]

Why don't we do by heron's formula sir