PQRS is a square.With centre P and radius =5cm an arc is drawn to cut SR at A and RQ at B.If AS=3cm then BR is equal to (a) 2cm (b) 1cm (c) 4cm (d) 3cm
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PQRS is a square.With centre P and radius =5cm an arc is drawn to cut SR at A and RQ at B.If AS=3cm then BR is equal to (a) 2cm (b) 1cm (c) 4cm (d) 3cm
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Verified answer
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Given :-
To Find :-
Solution :-
In right angle triangle PAS,
[tex] \angle \: S = 90 \degree[/tex]
By Pythagoras Theorem,
[tex] \to {PA }^{2} = {SA }^{2} + { PS}^{2} \\ \to {5}^{2} = {3}^{2} + { PS}^{2} \\ \to {PS}^{2} = 16 \\ \to \: PS = \sqrt{16} \\ \to \: PS = 4 \: cm[/tex]
In triangle PAS and triangle PBQ,
Hence, By SAS congruency,
PAS ≅ PBQ
Hence, It can be said as PS = QR = 4 cm and SA = QB = 3 cm.
Also,
BR = QR - QB
BR = 4 cm - 3 cm
BR = 1 cm
Final Answer :
@SweetestBitter