in a rectangle pqrs a and b are midpoints of the sides qr and rs respectively. if <pab=90 then ps:sr

Dear Student,
Please find below the solution to the asked query:


Given: In rectangle ABCD, QA=AR, SB=BR and PAB=90°PS:SR=?Let PS=QR=2a and PQ=SR=2bIn APQ,Using pythagoras theorem,AP2=PQ2+QA2AP2=2b2+a2AP2=4b2+a2       .....iIn ABR,Using pythagoras theorem,AB2=AR2+BR2AB2=a2+b2       .....iiIn PBS,Using pythagoras theorem,PB2=PS2+BS2PB2=2a2+b2PB2=4a2+b2       .....iiiNow, In APB,Using pythagoras theorem,PB2=PA2+AB24a2+b2=4b2+a2+a2+b22a2=4b2a2b2=42ab2=2ab=212a2b=21PSSR=21 or PS:SR=2:1

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