Question

In rectangle PQRS , diagonal QS = 26 and cot angle PQS = 1.5 . Find the area and the perimeter of rectangle PQRS

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Answer 1

Answer:

Please find below the solution to the asked query :

cot∠PQS=1.5=32⇒PQPS=32 (Since cot∠PQS=BasePerpendicular=PQPS)⇒PQ=3k and PS=2kPQ2+PS2=QS2(3k)2+(2k)2=(26)29k2+4k2=676k2=67613=52 cm2k=213−−√ cmSo, PQ=3×213−−√=613−−√ cmPS=2×213−−√=413−−√ cmArea of rectangle PQRS=PQ×PS=613−−√×413−−√=24×13=312 cm2Perimeter of rectangle PQRS=2(PQ+PS)=2(613−−√+413−