Many People Get This Wrong 🤯

Added: 2026-05-09

[00:00:00]Today we are going to solve a very interesting geometry problem where we are given an irregular shaped pentagon with some right angles and some side lengths and we need to find the value of X which is this side length. So, can you solve it? At first glance the figure looks complicated but the idea is to simplify it step by step by creating familiar shapes like rectangles and right triangles.

[00:00:25]Imagine a point F such that we draw a line FD parallel to AE and equal in length to AE.

[00:00:34]Similarly, we draw another line FA parallel to DE and equal in length to DE.

[00:00:42]By doing this we are essentially forming a rectangle FAED.

[00:00:47]This is because the opposite sides are equal in length by construction and also all four angles are 90°.

[00:00:54]Since DE is given as 7, FA also becomes 7.

[00:00:59]Similarly, since AE is 10, FD also becomes 10.

[00:01:05]Now look at the top slanted side.

[00:01:07]Originally from point D to C the length is 14 and now from F to D we have 10. So the full length from F to C becomes 10 + 14 which is 24. So now we can ignore the messy inner part and focus on a much simpler triangle.

[00:01:26]Next, connect point A to point C.

[00:01:30]This creates two triangles, triangle AFC and triangle ABC.

[00:01:37]Both are right triangles and both share the same side AC which will become very useful.

[00:01:43]Now focus on the triangle AFC.

[00:01:47]This is a right triangle with one side 7 and the other side 24. So we apply the Pythagorean theorem.

[00:01:54]24 squared plus 7 squared gives 576 plus 49 which is 625.

[00:02:04]Taking square root gives 25. So we get that AC is 25.

[00:02:10]Now shift the attention to the triangle ABC.

[00:02:14]This is also a right triangle.

[00:02:16]One side is X, the base we want to find.

[00:02:20]The other vertical side is 15 and the hypotenuse is 25 which we just found.

[00:02:26]Again, applying Pythagorean theorem, X squared plus 15 squared equals 25 squared.

[00:02:33]That gives X squared plus 225 equals 625.

[00:02:39]So we get X squared equals 625 minus 225 or 400. And taking square root gives X equals 20.

[00:02:51]So the value of X is 20 and that's it.

[00:02:55]Were you able to solve it?

[00:02:57]Like, share, and subscribe.

[00:03:01]So good.

[00:03:06]>> [music]