In the figure,PS is equals to 3, SQ is equal to 6, QR is equal to 5, PT is equal - Maths - Similarity

Question

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

Atul Shaw · Accepted Answer

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=PTPR⇒39=xx+y⇒x+y=3x⇒y=2xso, for x=1 y=2 and for x=2 y=4Therefore, (x,y)≡(1,2) and (2,4) are possible pairs

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.