Simple geometry puzzle involving triangles

[DanceMentor]

This one definitely requires a little knowledge about triangles. Do you remember the name of the theorem we must use to solve it?

 

[fiesta0618]

Good old Pythagoras!

But there is a shortcut here that meant I could solve this in 5 seconds with no pencil...which I guess the caption is expecting us to use?

Spoiler: Solution

There are only handful of special right triangles where all sides have integer lengths. The most famous of these is the 3:4:5 triangle.

Drop an altitude line through the shape to split it into rectangle & triangle, and we see the telltale 4 and 5. Boom, the last side must be 3, so x = 8.

 

[ProgressNotPerfection]

“What is x?”

That’s an easy one! X is the 24th letter of the English alphabet.

 

[IndyLady]

Why no pen or paper? Is the author trying to assert some sort of mental math superiority complex, or is that now considered cheating? I notice it doesn't say "no AI / ChatGPT / Google".

And yes, I got the answer, and yes with pen and paper, because I did math problems with pen(cil) and paper for almost 20 years (kingergarden through masters degree) and I'm not going to sit here and feel like I don't deserve full credit.

 

[joy]

I didn't know Fiesta's thing, just solved it in my head.

 

[ralf]

That was pretty easy, but you'll need decent visualization skills to do without pen(cil) and paper.

Spoiler

Split the shape into a rectangle and right triangle, which will give you x = 5 + 3