Question

71. In the given figure, PQRS is a trapezium with PQ|| SR and PQ = 15 cm and SR = 11 cm. If U is the mid point of PS and UV|| PQ, then the ratio of areas of PQVU and that of UVRS is equal to S PL 471 11:15 (2) 7:6 (3) 13:15 (4) 8:7

JEE/Engineering Exams

Maths

Solution

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Drow 2 pappendiculars flom somdk on PQ As U is the midit. and VCIIPA Using midpt theotwe we have Cis afso a mid So is ( D ). Srmilarily ( sin Delta operatorname{suc} ) and ( Delta operatorname{sen} A ) ( s c=frac{1}{2} s A ) midpt thesenn ( y ) ( therefore ) Ala of ( s v c=frac{1}{4} ) Similarly Ara of ( R D V=frac{1}{4} ) Alla ( oint R B varphi ) ( left.operatorname{Ratio}=frac{frac{3}{4}left(f frac{1}{2}(p A x s A)right)+frac{1}{2}(A B x S A)+frac{3}{4}left(frac{1}{2}(B Q x S A)right)}{frac{1}{4}left(frac{1}{2}(P A times S A)+frac{1}{2}(S R times S A)+frac{1}{L}left(frac{1}{2}(B Q times S A)right.right.}right) ) Since ( S R=A B ) [ frac{frac{3}{8}(P++B varphi)+frac{1}{2} A B}{frac{1}{8}(P A+B Q)+frac{1}{2} A B} quadleft(begin{array}{c} A B=11 P A+B varphi=15-11 end{array}right) ] ( =frac{frac{3}{2}+frac{11}{2}}{frac{1}{2}+frac{11}{2}}=7 / 6 ) ( operatorname{Ans} frac{1}{7} )