What's The SHORTEST Distance? – Math Puzzle

Added: 2026-05-12

[00:00:00]Hello my lovelies. It's Susanna and today I want to show you how to solve this problem. What is the shortest distance between the dog and its dog house? We have the dog here, its dog house here. We are given the length of this part, of this part, and of this part. We have a right angle here and here. And we have to find the shortest distance between the dog and its dog house. So the direct distance. If I go from the doghouse directly to the dog, this is the length we're looking for. And we've just created two triangles here and here. And they are even right triangles which is great because then we are allowed to use the Pythagorean theorem. But the problem is if we take a look at this triangle down here for example.

[00:01:04]Yes, we know the length of this part here. But we don't know the length of this part here because the 60 is the length of this entire side here, not just this part down here. So we don't know how long this is in this triangle, but maybe we don't use these two separate triangles. Maybe we just create one big triangle because we know the length of this side here. We can just go here and draw a line, a parallel line down here. So we know this is of length 60. And because here was a right angle, we know okay then we have a right angle here as well.

[00:02:02]And if we make this line here longer and because we had a right angle here, we also know that we have a right angle here.

[00:02:13]And now we have this big triangle, we know the length of this side. What about this part here? This is just the 15. So we even know the length of this part which means that we know the length of the entire side by taking 65 + 15 which equals 80. Then so now we have our triangle which is also a right triangle.

[00:02:49]We know the length of this side. We know the length of this side and we want to find the length of this side here. So let's call this length here x and let's use the Pythagorean theorem. Now for this we first have to find the hypotenuse. So that is the side that always lies across the right angle. So here across this here is the hypotenuse.

[00:03:16]And the Pythagorean theorem then says take one of the sides, so the 80, and square it plus take the length of the other side, the 60, and square it. And then you get the hypotenuse squared. So in our case, our x squared. And now we only have to solve this equation for x.

[00:03:43]Let's do some calculations on the left side. We have 80 squared here which is 80 * 80. So we can multiply 8 by 8 first which equals 64 and then we add these two zeros.

[00:04:02]The same thing with the 60 squared here which is 60 * 60. So we multiply 6 by 6 first which equals 36 and then we add these two zeros. On the other side we have our x²ared.

[00:04:22]If we add these two numbers we get 10,000 here. On the other side we have our x squared. And to solve for x now we only have to get rid of the square here. So let's take the square root on both sides of the equation. If we do that, we get two solutions for our x. A first positive solution x1 and a second negative solution x2.

[00:04:54]We have to find the square root of 10,000. Now we have this package of these two zeros here and this package of these two zeros here. So the 10,000 can be written as 100 * 100 which is 100 squared. So if we take the square root of 100 squared only the 100 is left here as a result. And then don't forget that you get the negative 100 as your negative solution here. But we don't need the negative solution here for our problem because our x is the length of this side here and it has to be positive. So we cannot use this negative solution here. But we don't need it. We only need it the distance the shortest distance from the dog to its dog house.

[00:05:54]And that is 100. If you like my video, please give it a thumbs up. It helps me a lot. I wish you a wonderful day and I hope to see you in one of my next videos. Take care.