Q. 54.1( 58 Votes )

In figure 2.30, p

Answer :

From figure,


In ∆PAT, PAT = 900


TP2 = AT2 + PA2 …1


In ∆AST, SAT = 900


TS2 = AT2 + SA2 …2


In ∆QBT, QBT = 900


TQ2 = BT2 + QB2 …3


In ∆BTR, RBT = 900


TR2 = BT2 + BR2 …4


TS2 + TQ2 = AT2 + SA2 + BT2 + QB2 [Adding 2 and 3]


TS2 + TQ2 = AT2 + PA2 + BT2 + BR2 [SA = BR, QB = AP]


TS2 + TQ2 = TP2 + TR2 [From 1 and 4]


PROVED.


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