Can you find the length X?

Added: 2026-05-28

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

[00:00:06]Angle CPB It will be equal to angle ABP That will be theta.

[00:00:22]This angle is theta.

[00:00:27]And now in triangle BCP It is B C P This angle is theta.

[00:00:54]This angle is theta.

[00:00:58]That means BC and CP, they will be equal.

[00:01:05]And BC is 10.

[00:01:07]So CP it will be also 10.

[00:01:14]CP is 10.

[00:01:24]And now from point B if we make a perpendicular on CD Suppose this point is Q, then ABQD it will be a rectangle.

[00:02:13]So, BQ it will be equal to AD that will be eight.

[00:02:26]And DQ it will be equal to AB that is five.

[00:02:37]So, BQ is eight.

[00:02:42]And DQ is five.

[00:02:50]And now in triangle BCQ BQ squared plus CQ squared it will be BC squared.

[00:03:15]And BQ is eight squared plus CQ squared.

[00:03:23]And BC is 10 squared.

[00:03:27]And 64 plus CQ squared is 100.

[00:03:39]So, CQ squared is 100 minus 64.

[00:03:47]And CQ squared is 36.

[00:03:52]That means CQ it will be six.

[00:03:59]CQ is six.

[00:04:06]And now PQ is CP minus CQ.

[00:04:28]And CP is 10 minus CQ is six.

[00:04:34]That will be four.

[00:04:37]PQ is four.

[00:04:40]And DP plus PQ is DQ.

[00:04:49]And DP is X plus PQ is four.

[00:04:54]And DQ is five.

[00:04:58]So X will be five minus four.

[00:05:03]That means X is one.

[00:05:10]>> [music]