Can you find the length X in the triangle?

Indexed: 2026-05-16

[00:00:00]Can you find the length x?

[00:00:05]In the triangle ABP this angle is theta.

[00:00:14]This angle is 90° so this angle will be 90° - theta.

[00:00:28]And in the triangle ACP this angle is 2 theta.

[00:00:38]So this angle will be 90° - 2 theta.

[00:00:49]And now in the triangle ABC it is A B C this angle is 90° - theta.

[00:01:19]And this angle is theta + 90° - 2 theta.

[00:01:29]That will be 90° - theta.

[00:01:36]And these two angles are equal.

[00:01:41]That means AC and BC they will be also equal.

[00:01:48]And BC is x + 1.

[00:01:55]BC is x + 1.

[00:01:58]So AC it will be also X + 1.

[00:02:06]AC is X + 1.

[00:02:11]And now AB squared it is AB squared BP is squared.

[00:02:39]And also AP squared it is AC squared - CP is squared.

[00:02:53]So from these two equations we can say that AB squared - BP squared is equal to AC squared CP is squared.

[00:03:17]And AB is 5 is squared BP is 1 is squared.

[00:03:27]AC is X + 1 is squared - CP is X is squared.

[00:03:39]And 25 - 1 it is X is squared + 2X + 1 X is squared.

[00:03:55]and x is squared will get cancelled.

[00:04:02]So 24 it is 2x + 1 so 2x it will be 24 minus 1 that is 23 so x will be 23 divided by 2.

[00:04:32]>> [music]