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You can eliminate y=0 immediately because you know that y is a positive number. It's the length of a line in your diagram.

I wish I had you as a teacher when I was young. I'm 74 and re-discovering math. You are an angel.

That moment you catch yourself watching a math video on Spring Break lol

I am not a Math person, but I find the video interesting enough to jump start my aged brain 😊

When the right triangle was drawn with the hypotenuse measuring length 5, my brain immediately registered the 3-4-5 special right triangle, specifying side y=4 and side (5-x)=3. This immediately made x=2.

This video is so relaxing. I could listen to her voice forever.

The true challenge of this math problem is to learn it in high school, forget it for twenty years, then revisit these concepts in a YouTube video.  Thank you for jogging this part of my brain that hasn’t been used in decades.

This is a good one! I noticed the distance you're calling y is also equal to 5-x/2 which means (5-x)^2 + (5-x/2)^2 = 25. This simplifies to x^2 - 12x + 20 = 0 which factors to (x-2)(x-10) = 0. The solution 10 is too large for the geometry, so x must be 2 and the area is 2^2 = 4.

Knowledge of math is like a magical power.  It allows you to do things which otherwise seem impossible.

Love your videos. Can't understand people who don't like math. Has been my favorite subject since ever.

instead of finding y with the substitution and replacing x, I found x and replaced y.
Sussanne found x=10-2y, I got y=(x-10)/-2 and substituted, then found x directly.
Seems like a tad less work, but both are valid methods.

I wasn’t looking to revisit math class when your video popped into my feed but now I’m addicted. I see a video of yours and I click. And I’m getting better at recognizing next steps! :)

I have a confession to make. When I first saw thumbnails of your videos appearing on my feed, I was a bit skeptical: I got the vibe of "channel that soullessly presents the answer to loads of random maths problems because the algorithm rewards this". Then I saw a clip of someone interviewing you, where it started to be clearer that you have a genuine human interest in what you do. And now I've watched this video - and I'm really impressed!! Your explanations are slow and clear and made easy to follow, while not dumbing down on rigour and depth of insight. Can I hazard a guess that you did your mathematics training in Germany? I'm a mathematician based in the UK, and I don't think that UK or US students would be as rigorous as you have been in solving a geometry problem like this.

I did it a slightly different way, but got the same answer as you! I love your little challenges. They are fun dessert after a day of meaningless work.

Thank you, Susanne.  ❤❤

You never fail to impress me. I learn something new every time I watch your videos. I love math, but sometimes the answer isn't quite so apparent to me. I have now made a playlist of your videos so I can more easily reference a video relevant to what I am studying. I think you're awesome. Thank you, my lovely!

There is a more simple way: 25 = (5 - x)^2 + (5 - x/2)^2,  x = 2 , 10

Why do i watch your videos after i have had an evenings drinking ??? hahaha .. but i did getted ? gotted 4  two !

I wished there are more teachers like you that can explain things in such a pleasant and easy-to-understand fashion. Thank you!