In the figure,PS is equals to 3, SQ is equal to 6, QR is equal to 5, PT is equal to x and TR is equals to y. Give any two pairs of value of x and y such that line ST is parallel to side QR.

Solution:PS=3 and SQ=6; PT=x and TR=yAs, ST||QRSo, PST=PQR (Corresponding angles)Also, PTS=PRQ (Corresponding angles)In tri. PST and tri. PQR,P (Common)PST=PQR (From above)PTS=PRQ (From above)So, by AAA criterion both triangle are similar.So, PSPQ=PTPR39=xx+yx+y=3xy=2xso, for x=1 y=2 and for x=2 y=4Therefore, (x,y)(1,2) and (2,4) are possible pairs

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