Question

please solve this question.the answer BP/AB=√2-1/√2

Answer 1

I hope this will help you

Answer 2

Answer:

(√2 - 1) / (√2)  

Step-by-step explanation :

Let area of triangle be x

therefore, area of [] PQBC will also be x

                           

Here triangle APQ and triangle ABC are similar since PQ || BC

we know,

( area of triangle APQ ) / ( area of triangle ABC ) = [( AP )^2] / [( AB )^2]

=> { x/(x+x) }^(1/2) = AP / AB

=> 1/√2 = AP / AB

=> AP/( AP + BP ) = 1/√2

=>( AP + BP )/AP = √2

=> 1 + BP/AP = √2

=> BP/AP = (√2 - 1)

=> AP/BP = 1/(√2 - 1)

=> ( AB - BP ) / BP = 1/(√2 - 1)

=> ( AB/BP ) - 1 = 1/(√2 - 1)

=> ( AB/BP ) = { 1/(√2 - 1) } + 1

=> ( AB/BP ) = (√2) / (√2 - 1)

=> BP/AB = (√2 - 1) / (√2)                                [ DONE ]